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We adopt extreme value theory to estimate the upper limit of the next record‐breaking magnitudes of induced seismic events. The methodology is based on order statistics and does not rely on knowledge of the state of the subsurface reservoir or injection strategy. The estimation depends on the history of record‐breaking events produced by the anthropogenic activities. We apply the methodology to three different types of industrial operations: natural gas production, saltwater disposal and hydraulic fracturing. We show that the upper limit estimate provides a reliable and realistic upper bound for magnitudes of the record‐breaking events in investigated datasets including 15 publicly available datasets. The predicted magnitudes do not overestimate the observed magnitudes by more than 1.0 magnitude unit and underestimation is rare, probably resulting from insufficient sampling of the statistical distribution of the induced seismicity. The richest dataset, sourced from downhole and surface monitoring of the Preston New Road hydraulic fracturing, provides reliable estimates of the magnitudes over three orders of magnitudes with only slight underprediction of the largest observed event. While the detection of weaker events improves the performance of the method, we show that it can be applied even with a few observed record‐breaking events to provide reliable estimates of magnitudes. However, care must be taken to ensure that event catalogues are estimated consistently across a range of magnitudes. [ABSTRACT FROM AUTHOR]

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost‐effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation‐Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS‐based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older. [ABSTRACT FROM AUTHOR]

In many industries, the reliability of a product is often determined by a quantile of a distribution of a product's characteristics meeting a specified requirement. A typical approach to address this is to assume a parametric model and compute a one‐sided confidence bound on the quantile. However, this can become difficult if the sample size is too small to reliably estimate such a parametric model. Linear interpolation between order statistics is a viable nonparametric alternative if the sample size is sufficiently large. In most cases, linear extrapolation from the extreme order statistics can be used, but can result in inconsistent coverage. In this work, we perform an empirical study to generate robust weights for linear extrapolation that greatly improves the accuracy of the coverage across a feasible range of distribution families with positive support. Our method is applied to two industrial datasets. [ABSTRACT FROM AUTHOR]

The use of joint models for item scores and response times is becoming increasingly popular in educational and psychological testing. In this paper, we propose two new person‐fit statistics for such models in order to detect aberrant behaviour. The first statistic is computed by combining two existing person‐fit statistics: one for the item scores, and one for the item response times. The second statistic is computed directly using the likelihood function of the joint model. Using detailed simulations, we show that the empirical null distributions of the new statistics are very close to the theoretical null distributions, and that the new statistics tend to be more powerful than several existing statistics for item scores and/or response times. A real data example is also provided using data from a licensure examination. [ABSTRACT FROM AUTHOR]

It is verified that the maximum likelihood (ML) estimators of the standard two‐sided power distribution (STSP) parameters introduced by van Dorp and Kotz on the interval (0,1) can be severely biased. Since the usual analytical methods of bias correction cannot be applied in such a parametric distribution, bootstrap bias correction methods are proposed. The numerical study favors a particular bootstrap estimator based on parametric resampling. Real data applications are also considered to illustrate the impact of bias correction of the usual maximum likelihood estimators of the standard two‐sided power distribution parameters when the sample size is small. [ABSTRACT FROM AUTHOR]

Dielectric breakdown (BD) is known to cause component failure in electronic devices and high‐voltage power lines over many decades. In recent years, this failure mechanism has been exploited to intentionally form nanoscale filaments in resistive random‐access‐memory (ReRAM) devices for artificial intelligence (AI). The statistical nature of this failure mechanism, known as the inverse size scaling law based on the weakest‐link theory, dictates the ever‐higher forming voltages for ReRAM devices, in turn, requiring additional peripheral transistors. This law also causes diminishing lifetimes of electronic components for future generations of very‐large‐integrated circuits (VLSI) technology. Currently, the semiconductor industry faces these scaling barriers limiting the miniaturization of both VLSI and AI hardware technology. Here, experimental evidence of a reverse area dependence is presented by introducing an innovative fabrication process with a hydrogen‐plasma‐treated layer in a bilayer HfO2 structure. Using joint order statistics rather than traditional extreme‐value statistics, a physics‐based statistical model is developed in agreement with the experimental data, thus demonstrating that there is no fundamental reason preventing this law from being reversed or altered. These findings will have a significant impact on both technology scaling and fabrication innovation for electronic and/or bioinspired nanomaterials; moreover, stimulate much research in physics, statistics, and reliability. [ABSTRACT FROM AUTHOR]

Chemical risk assessment is important for risk management, and estimates of chemical exposure must be as accurate as possible. Chemical concentrations in food below the limit of detection are known as nondetects and result in left‐censored data. During statistical analysis, the method used for handling values below the limit of detection is important. Many risk assessors employ widely used substitution methods to treat left‐censored data, as recommended by international organizations. The National Institute of Food and Drug Safety Evaluation of South Korea also recommends these methods, which are currently used for chemical exposure assessments. However, these methods have statistical limitations, and international organizations recommend more advanced alternative statistical approaches. In this study, we assessed the validity of currently used statistical methods for handling nondetects. To identify the most suitable statistical method for handling nondetection, we created virtual data and conducted simulation studies. Based on both simulation and case studies, the Maximum Likelihood Estimation (MLE) and Robust Regression on Order Statistics (ROS) methods were found to be the best options. The statistical values obtained from these methods were similar to those obtained from the commonly used 1/2 Limit of Detection (LOD) substitution method for nondetection treatment. In three case studies, we compared the various methods based on the root mean squared error. The data for all case studies were from the same source, to avoid heterogeneity. Across various sample sizes and nondetection rates, the mean and 95th percentile values for all treatment methods were similar. However, "lognormal maximum likelihood estimation" method was not suitable for estimating the mean. Risk assessors should consider statistical processing of monitoring data to reduce uncertainty. Currently used substitution methods are effective and easy to apply to large datasets with nondetection rates <80%. However, advanced statistical methods are required in some circumstances, and national guidelines are needed regarding their use in risk assessments. [ABSTRACT FROM AUTHOR]

Summary: This paper provides a framework for testing multiple null hypotheses simultaneously using experimental data in which simple random sampling is used to assign treatment status to units. Using general results from the multiple testing literature, we develop under weak assumptions a procedure that (i) asymptotically controls the familywise error rate—the probability of one or more false rejections—and (ii) is asymptotically balanced in that the marginal probability of rejecting any true null hypothesis is approximately equal in large samples. Our procedure improves upon classical methods by incorporating information about the joint dependence structure of the test statistics when determining which null hypotheses to reject, leading to gains in power. An important point of departure from prior work is that we exploit observed, baseline covariates to obtain further gains in power. The precise way in which we incorporate these covariates is based on recent results from the statistics literature in order to ensure that inferences are typically more powerful in large samples. [ABSTRACT FROM AUTHOR]

Background: Development of skin cancer, in particular melanoma, has been linked to sex hormones. We aimed to determine the incidence of skin cancer in transgender individuals receiving gender‐affirming hormone treatment (GAHT). Methods: In this nationwide retrospective cohort study, clinical information of participants who visited our clinic between (the years) 1972 and 2018 and received GAHT was integrated with national pathology and cancer statistics data in order to assess skin cancer incidence. Standardized incidence ratios (SIRs) were calculated. Results: The cohort consisted of 2,436 trans women and 1,444 trans men. The median age at the start of GAHT was 31 years (IQR 24–42) in trans women and 24 years (IQR 20–32) in trans men. The median follow‐up time for trans women was 8 years (IQR 3–18) with a total follow‐up time of 29,152 years and 4 years (IQR 2–12) with a total follow‐up time of 12,469 years for trans men. Eight trans women were diagnosed with melanoma (SIR 1.80 [95% CI 0.83–3.41] vs. all men; SIR 1.40 [0.65–2.65] vs. all women), and seven developed squamous cell carcinoma (SIR 0.78 [0.34–1.55] vs. all men; SIR 1.15 [0.50–2.27] vs. all women). Two trans men developed melanoma (SIR 1.05 [0.18–3.47] vs. all men; SIR 0.77 [0.14‐2.70] vs. all women). Conclusions: GAHT did not appear to affect skin cancer incidence in this large cohort of transgender individuals. As skin cancer incidence increases with age and the proportion of elderly subjects is currently limited in this cohort, it will be worthwhile to repeat this analysis in the future. [ABSTRACT FROM AUTHOR]

In this article, we will address the complexity of non‐identical components in multi‐component systems. Most technical systems can be described as such since either component types or component functions within the system vary amongst components. While most reliability related work resorts to the assumption of homogeneous components, we aim to address the often more realistic assumption of heterogeneous components extending the model of Extended Sequential Order Statistics by two inferential methods. Firstly, the derivation of Maximum Likelihood Estimates including a simulation study demonstrating their good performance for large enough sample size. Secondly, we introduce a likelihood ratio test to test whether components can be assumed identical accompanied by a power study. Both methods are powerful tools in reliability contexts. The former increases our understanding of component behaviour, especially upon failure of other components. This knowledge empowers system operators to make better decisions regarding maintenance schedules and failure time prediction. The latter supports operators in their quest of identifying component equivalence. Therefore, both methods can be used to achieve meaningful results in real life applications. [ABSTRACT FROM AUTHOR]

E‐Bayesian inference is of incremental significance in the area related to the reliability of industrial products dealing with censored data sets. In this article, based on the progressive Type‐II right censored order statistics (PTIIRCOS), the E‐Bayesian estimates (E‐BE) for the parameters of Gompertz distribution (GD) and its hazard function are obtained and compared with the maximum likelihood (MLE) and Bayesian (BE) estimates. The squared error loss function (SE), linear‐exponential loss function (LINEX), and Al‐Bayyati loss function (ALB) are considered for the methods of BE and E‐BE. Some properties for the E‐BE estimates are discussed based on PTIIRCOS. Real data is established to clear the theoretical procedures. Akaike information criterion (AIC) is used to prove that GD is the best to model the data compared to other competitors and could potentially be very adequate in describing and modeling industrial products data. Finally, simulation study has been operated for comparing the E‐BEs with the MLEs and BEs. [ABSTRACT FROM AUTHOR]

In manufacturing systems, statistical process control (SPC) is used to detect unusual observations in the process. Most control charts are composed based on the normality assumptions of the observations. However, checking the normality assumption in multivariate control systems cannot be practical in real‐life applications. As a result, we propose a nonparametric bivariate cumulative sum control chart (CUSUM) based on exceedance statistics for detecting the shifts in location parameters. Since the proposed chart (BCUSUM‐EX) relied on exceedance statistics and is nonparametric, the use of the chart is straightforward and practical for users. Moreover, due to the nature of CUSUM charts, the proposed chart contains information about historical and current observations. The performance of the BCUSUM‐EX chart is compared with the spatial sign CUSUM (SS‐CUSUM) control chart under some well‐known bivariate distributions such as bivariate normal, t, and gamma. The BCUSUM‐EX chart's performance is better than the SS‐CUSUM control chart regarding run length characteristics. Lastly, to show the importance of the proposed control chart, the BCUSUM‐EX chart has been applied to the aluminium electrolytic capacitor manufacturing process. [ABSTRACT FROM AUTHOR]

In this paper, we propose new asymptotic confidence intervals for extreme quantiles, that is, for quantiles located outside the range of the available data. We restrict ourselves to the situation where the underlying distribution is heavy‐tailed. While asymptotic confidence intervals are mostly constructed around a pivotal quantity, we consider here an alternative approach based on the distribution of order statistics sampled from a uniform distribution. The convergence of the coverage probability to the nominal one is established under a classical second‐order condition. The finite sample behavior is also examined and our methodology is applied to a real dataset. [ABSTRACT FROM AUTHOR]

The presence of Homo floresiensis and Homo luzonensis in southeast Asia 90,000 to 60,000 years ago is considered surprising by many, and has been used to support their designation as unique species and the islands they were discovered on as refugia. Here, we statistically test the null hypothesis that H. floresiensis and H. luzonensis represent temporally uninterrupted occurrences relative to Homo erectus. We do this using the 'surprise test' for the exceptionality of a new record. Results demonstrate that H. floresiensis and H. luzonensis are not temporally distinct relative to H. erectus. Their late persistence should, therefore, not be considered surprising, they cannot reliably be inferred to be outside of H. erectus' temporal range, and – temporally – the islands of Luzon and Flores are not supported as refugia. Similarly, late H. erectus at Ngandong, Java, is not demonstrated to be temporally distinct relative to earlier, principally mainland‐Asian, H. erectus. Further, we demonstrate that substantial numbers of fossil discoveries would be needed before H. floresiensis and H. luzonensis are outside of H. erectus' expected temporal range. If H. floresiensis and H. luzonensis are descended from H. erectus populations, our results point toward either geographic processes of allopatric speciation or behavioural processes leading to a sympatric speciation event. [ABSTRACT FROM AUTHOR]

A common method of checking person‐fit in Bayesian item response theory (IRT) is the posterior‐predictive (PP) method. In recent years, more powerful approaches have been proposed that are based on resampling methods using the popular Lz∗$L_{z}^{*}$ statistic. There has also been proposed a new Bayesian model checking method based on pivotal discrepancy measures (PDMs). A PDM T is a discrepancy measure that is a pivotal quantity with a known reference distribution. A posterior sample of T can be generated using standard Markov chain Monte Carlo output, and a p‐value is obtained from probability bounds computed on order statistics of the sample. In this paper, we propose a general procedure to apply this PDM method to person‐fit checking in IRT models. We illustrate this using the Lz$L_{z}$ and Lz∗$L_{z}^{*}$ measures. Simulation studies are done comparing these with the PP method and one of the more recent resampling methods. The results show that the PDM method is more powerful than the PP method. Under certain conditions, it is more powerful than the resampling method, while in others, it is less. The PDM method is also applied to a real data set. [ABSTRACT FROM AUTHOR]

The present review provides a survey on basic models of ordered data and censoring mechanisms with a focus on lifetime data, failure data, and reliability applications. Throughout, illustrations of the data generation process as well as of the censoring mechanisms are used to visualize these procedures. By example we present basic results assuming a life testing model with independent and identically distributed measurements and focus on selected inferential results for exponentially distributed lifetimes. In particular, we aim to illustrate similarities between the models as well as to highlight some interesting exact statistical results. It is not intended to survey all possible model assumptions, probabilistic results, and used inferential methods used in this framework. For this purpose as well as for further reading, we provide an extensive bibliography. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Reliability, Survivability, and Quality ControlAlgorithms and Computational Methods > Maximum Likelihood MethodsData: Types and Structure > Traditional Statistical Data [ABSTRACT FROM AUTHOR]

A first‐order finite‐state Markov chain (FSMC) typically models the Rayleigh fading channel in the open literature because the first‐order FSMC is analytically tractable and can derive closed‐form results. Non‐orthogonal multiple access (NOMA) has been recognised as a novel wireless technology that addresses challenges in the next generation of mobile communications. According to the power‐domain NOMA protocol, channels in the NOMA wireless network are sorted by the channel gain. Then considering NOMA, there is insufficient information on how to further form a suitable model for ordered Rayleigh fading channels based on the first‐order FSMC. Given the mathematical statement on how to model the order statistics of multidimensional Markov chains for ordered Rayleigh fading channels, the authors consider these order statistics as a Markov chain, and propose specific processes of representing the state space and constructing the transition probability matrix accordingly. Numerical and simulation results validate the mathematical correctness and accuracy of these novel processes. In addition, for ordered Rayleigh fading channels, the performances of various methods of partitioning the entire signal‐to‐noise ratio range are compared. The performance comparison results are the same as those obtained for the individual unordered Rayleigh fading channel. [ABSTRACT FROM AUTHOR]

In this study, we develop comprehensive symbolic interval‐valued time‐series models, including interval‐valued moving average, auto‐interval‐regressive moving average, and heteroscedastic volatility models. These models can be flexibly combined to adapt more effectively to various situations. To make inferences regarding these models, likelihood functions were derived, and maximum likelihood estimators were obtained. To evaluate the performance of our methods empirically, Monte Carlo simulations and real data analyses were conducted using the S&P 500 index and PM2.5 levels of 15 stations in southern Taiwan. In the former case, it was found that the proposed model outperforms all other existing methods, whereas in the latter case, the residuals deduced from the proposed models provide more intuitively appealing results compared to the conventional vector autoregressive models. Overall, our findings strongly confirm the adequacy of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we discuss stochastic comparison of the largest order statistics arising from two sets of dependent distribution‐free random variables with respect to multivariate chain majorization, where the dependency structure can be defined by Archimedean copulas. When a distribution‐free model with possibly two parameter vectors has its matrix of parameters changing to another matrix of parameters in a certain mathematical sense, we obtain the first sample maxima is larger than the second sample maxima with respect to the usual stochastic order, based on certain conditions. Applications of our results for scale proportional reverse hazards model, exponentiated gamma distribution, Gompertz–Makeham distribution, and location‐scale model, are also given. Meanwhile, we provide two numerical examples to illustrate the results established here. [ABSTRACT FROM AUTHOR]

Summary: In this article, we study a new generator of distributions called the odd JCA‐G family. We determine the main mathematical properties of the new family. Some special submodels of the odd JCA‐G family are presented. The special models of the JCA‐G family have tractable densities shapes which possess various kinds of asymmetric, reversed‐J, left‐skewed, right‐skewed, symmetrical shapes. Furthermore, special submodels exhibit flexible hazard rate shapes. Additionally, the parameters of the odd JCA Burr‐XII model are estimated using some classical estimation approaches. The performance and efficiency of these approaches are explored via numerical simulations. The applicability of the odd JCA‐G family is illustrated by fitting two real‐life datasets. The data analysis shows that the odd JCA Burr‐XII model outperforms some well‐known distributions for the selected data. [ABSTRACT FROM AUTHOR]

Complex computational engineering uncertainty analyses have become more prevalent. When input parameters of such engineering models are uncertain, the output metric's uncertainty distribution is of an unknown parametric form. Since Wilks' method, named after the seminal paper by SS Wilks in 1941 entitled "Determination of sample sizes for setting tolerance limits", is a nonparametric statistical procedure, it has received renewed interest, in particular in nuclear and chemical safety engineering. Unfortunately, the prevailing Wilks' method applied relies on arbitrary specification of order statistics' ranks with undue influence on the sample size recommendations that follow. Herein, a novel modification of Wilks' method involving two quantiles is proposed resolving that arbitrary rank selection. Together with a confidence level to be exceeded, these quantiles uniquely determine the parameters of an order statistics' beta distribution which drive the selection of symmetric tolerance limits. The modified procedure is demonstrated in two illustrative engineering uncertainty analysis examples drawn from the nuclear and chemical engineering domains. [ABSTRACT FROM AUTHOR]

Polarimetric synthetic aperture radar (POLSAR) systems provide high resolution images containing polarimetric information. So, they have high capability in land cover classification. In this work, a binary coding‐based polarimetric‐morphological (BCPM) feature extraction is proposed for POLSAR image classification. At first, a set of polarimetric features is proposed. Then, a new morphological framework is introduced for contextual feature extraction from the POLSAR cube. The coherence matrix is composed from diagonal and non‐diagonal elements with different information. These elements are analysed separately in the proposed method. Moreover, the amplitude and phase components of the non‐diagonal elements are individually analysed using morphological filters by reconstruction. Finally, a binary coding‐based polarimetric‐spatial feature reduction, which uses the first order statistics, is proposed for feature transformation. The experiments on three real POLSAR images and a synthetic dataset show the superior performance of BCPM compared to several classification methods. [ABSTRACT FROM AUTHOR]

It is well known that sample moments are more sensitive and less robust than order statistics for robustness with respect to outliers. In this article, we show that the situation is exactly the opposite for robustness with respect to rounding. For large and very large sample sizes, statistical procedures based on order statistics become non‐applicable even for very mild data rounding while procedures based on sample moments work perfectly for this rounding level. The comparison of sample moments and order statistics is made for tests for normality and tests for exponentiality. [ABSTRACT FROM AUTHOR]

In this paper, an F-type test is proposed for the functional association between a functional covariate and a scalar response in functional linear models (FLM). The proposed F test is based on the order statistics of functional principal components (fPCs), which is motivated by the phenomena that the power of the classical F test is sensitive to the choice of thresholds. Theoretical properties of the proposed test are established under both the null and alternative hypotheses, especially showing that it can detect the local alternative of order Sn1/4n-1/2, that is, the fastest rate in the highdimensional linear model, where n and Sn are the sample size and the number of fPCs, respectively. Extensive simulation studies are conducted to demonstrate the finite sample performance, showing advantages to the existing tests. Moreover, our procedure is applied to a real data analysis related to the diffusion tensor imaging tractography study. [ABSTRACT FROM AUTHOR]

Stochastic micro‐patterns successfully enhance the realism of virtual scenes. Procedural models using noise combined with transfer functions are extremely efficient. However, most patterns produced today employ 1D transfer functions, which assign color, transparency, or other material attributes, based solely on the single scalar quantity of noise. Multi‐dimensional transfer functions have received widespread attention in other fields, such as scientific volume rendering. But their potential has not yet been well explored for modeling micro‐patterns in the field of procedural texturing. We propose a new procedural model for stochastic patterns, defined as the composition of a bi‐dimensional transfer function (a.k.a. color‐map) with a stochastic vector field. Our model is versatile, as it encompasses several existing procedural noises, including Gaussian noise and phasor noise. It also generates a much larger gamut of patterns, including locally structured patterns which are notoriously difficult to reproduce. We leverage the Gaussian assumption and a tiling and blending algorithm to provide real‐time generation and filtering. A key contribution is a real‐time approximation of the second order statistics over an arbitrary pixel footprint, which enables, in addition, the filtering of procedural normal maps. We exhibit a wide variety of results, including Gaussian patterns, profiled waves, concentric and non‐concentric patterns. [ABSTRACT FROM AUTHOR]

The study evaluates OpenFOAM's adaptive mesh refinement (AMR) capabilities and accuracy when applied to numerical simulations of turbulent buoyant flows. To this purpose, large eddy simulations of Sandia's turbulent helium plume test case are considered, a scenario with similar characteristics (in terms of air entrainment and vortex shedding) to those encountered in large‐scale fires. Comparison is made of the relative accuracy (in terms of both first and second order statistics), the predicted puffing frequencies and the computing times of numerical simulations using AMR and static meshes. Additionally, a sensitivity study on different AMR parameters is conducted and an evaluation of the performance of the dynamic Smagorinsky model when combined with AMR is made. Overall, the predictions of AMR are very satisfactory, in terms of both accuracy and computing times, compared to the use of static meshes of different sizes. Nevertheless, it is observed that a careful choice of a static mesh can result in equally accurate predictions with comparable, or even smaller, computing times than AMR for the case at hand. Additionally, the use of AMR slightly modified the entrainment characteristics in the near‐field region of the plume and (significantly) altered some of the, dynamically determined, turbulence model parameters. [ABSTRACT FROM AUTHOR]

The Plackett‐Luce model (PL) for ranked data assumes the forward order of the ranking process. This hypothesis postulates that the ranking process of the items is carried out by sequentially assigning the positions from the top (most liked) to the bottom (least liked) alternative. This assumption has been recently relaxed with the Extended Plackett‐Luce model (EPL) through the introduction of the discrete reference order parameter, describing the rank attribution path. By starting from two formal properties of the EPL, the former related to the inverse ordering of the item probabilities at the first and last stage of the ranking process and the latter well‐known as independence of irrelevant alternatives (or Luce's choice axiom), we derive novel diagnostic tools for testing the appropriateness of the EPL assumption as the actual sampling distribution of the observed rankings. These diagnostic tools can help uncovering possible idiosyncratic paths in the sequential choice process. Besides contributing to fill the gap of goodness‐of‐fit methods for the family of multistage models, we also show how one of the two statistics can be conveniently exploited to construct a heuristic method, that surrogates the maximum likelihood approach for inferring the underlying reference order parameter. The relative performance of the proposals, compared with more conventional approaches, is illustrated by means of extensive simulation studies. [ABSTRACT FROM AUTHOR]

This study provides new identification and estimation results for ascending (traditional English or online) auctions with unobserved auction‐level heterogeneity and an unknown number of bidders. When the seller's reserve price and two order statistics of bids are observed, we derive conditions under which the distributions of buyer valuations, unobserved heterogeneity, and number of participants are point identified. We also derive conditions for point identification in cases where reserve prices are binding and present general conditions for partial identification. We propose a nonparametric maximum likelihood approach for estimation and inference. We apply our approach to the online market for used iPhones and analyze the effects of recent regulatory changes banning consumers from circumventing digital rights management technologies used to lock phones to service providers. We find that buyer valuations for unlocked phones dropped by 39% on average after the unlocking ban took effect, from $231.30 to $141.50. [ABSTRACT FROM AUTHOR]

Earth system models (ESMs) and mesoscale models have come to employ increasingly complex parameterization schemes for the atmospheric boundary layer, requiring surface boundary conditions for numerous higher order turbulence statistics. Of particular interest is the potential temperature variance (PTV), which is used not only as a boundary condition itself but also to close boundary conditions of other statistics. The existing schemes in ESMs largely rely on the assumptions of Monin‐Obukhov similarity theory (MOST) and are not necessarily applicable over complex and heterogeneous surfaces where large scale circulations and roughness sub‐layer effects may cause deviations from MOST. The National Ecological Observation Network is used here to evaluate existing parameterizations for the surface boundary of PTV, note key deficiencies, and explore possible remedies. The results indicate that existing schemes are acceptable over a variety of surface conditions provided the analysis of a priori filters out low frequency variability not associated with turbulent time scales. There was, however, significant inter‐site variability in observed similarity constants and a significant bias when compared to the textbook values of these parameters. Existing models displayed the poorest performance over heterogeneous sites and rough landscapes. Attempts to use canopy structure and surface roughness characteristics to improve the results confirmed a relation between these variables and PTV but failed to significantly improve the predictive power of the models. The results did not find strong evidence indicating that large scale circulations caused substantial deviations from textbook models, although additional analysis is required to assess their full impacts. Plain Language Summary: Modern models of the lower atmosphere, which are used to analyze climate change and weather, resolve increasingly complex characteristics of the turbulence in the atmosphere. An estimate for the value of many of these characteristics at the land surface is required to set boundary conditions for these models. An important boundary condition is the variance of very small temperature fluctuations that occur in the atmosphere due to turbulence. Currently, model estimates for these values assume the surface is flat and its characteristics do not change in space, which does not represent many of the conditions we wish to model over the earth. In addition, existing studies tend to only analyze data from a small number of locations. We analyzed data from a network of 39 sites and found that the current estimates work fairly well across a large variety of conditions, but that there is a bias in the constants often used and there are notable differences over forests, complex surfaces, and heterogeneous terrain. There is a clear relationship between surface characteristics such as tree canopy height and the performance of the model, however, it was not clear enough to improve our ability to predict the surface boundary condition. Key Points: Models of potential temperature variance in the surface layer based on similarity theory were evaluated using data from 39 varied sitesExisting schemes perform well across most surfaces, although the data shows a significant bias in the values of the similarity constantsCanopy structure and surface heterogeneity drive a large portion of inter‐site variability in model performance [ABSTRACT FROM AUTHOR]

Expectiles and quantiles can both be defined as the solution of minimization problems. Contrary to quantiles though, expectiles are determined by tail expectations rather than tail probabilities, and define a coherent risk measure. For these two reasons in particular, expectiles have recently started to be considered as serious candidates to become standard tools in actuarial and financial risk management. However, expectiles and their sample versions do not benefit from a simple explicit form, making their analysis significantly harder than that of quantiles and order statistics. This difficulty is compounded when one wishes to integrate auxiliary information about the phenomenon of interest through a finite‐dimensional covariate, in which case the problem becomes the estimation of conditional expectiles. In this paper, we exploit the fact that the expectiles of a distribution F are in fact the quantiles of another distribution E explicitly linked to F, in order to construct nonparametric kernel estimators of extreme conditional expectiles. We analyze the asymptotic properties of our estimators in the context of conditional heavy‐tailed distributions. Applications to simulated data and real insurance data are provided. [ABSTRACT FROM AUTHOR]

The outbreak of Covid‐19 in China during the Spring Festival of 2020 has changed life as we knew it. To explore its impact on China's economy, we analyse the daily railway passenger volume data during the Spring Festival travel rush and establish two RegARMA models to predict GDP in the first quarter. The models forecast China might lose 4.8 trillion yuan in the first quarter of 2020 due to Covid‐19, an expected decrease of 20.69 percent (year‐on‐year drop 15.60 percent). However, comparing our forecast GDP without Covid‐19 (23.2 trillion yuan) with the real GDP (20.65 trillion yuan), there is a smaller drop of 2.55 trillion yuan, a gap of 12.35 percent. The reason for this overestimation is that some positive factors, including macro‐control policies, are neglected in these models. With the global spread of Covid‐19, China should adopt a policy of focusing on balancing both domestic and external affairs against the instability of the world economy. [ABSTRACT FROM AUTHOR]

In most applications, parametric monitoring schemes are used to monitor the majority of industrial and nonindustrial processes in order to improve the quality of the outputs or services. However, parametric monitoring schemes are known to underperform when the normality assumption is not met or when there is not enough information about the symmetry or asymmetry nature of the process underlying distribution. Hence, in this paper, a new nonparametric Phase II Shewhart-type double-sampling (DS) monitoring scheme based on the precedence statistic is proposed in order to efficiently monitor quality processes when the underlying process distribution departs from normality. The performance is investigated using the average run length (ARL), standard deviation of the run length (SDRL), expected ARL (EARL) and expected average number of observations to signal (EANOS), and the average sample sizes (ASS) metrics. The latter metrics are computed using Monte Carlo simulation and exact formulae. In general, it is shown that the new DS precedence scheme outperforms the existing basic Shewhart precedence scheme with and without supplementary runs rules in many situations. A real-life illustrative example based on a filling process of milk bottles is provided to demonstrate the application and implementation of the new DS precedence monitoring scheme. [ABSTRACT FROM AUTHOR]

Recently, the two‐parameter Chen distribution has widely been used for reliability studies in various engineering fields. In this article, we have developed various statistical inferences on the composite dynamic system, assuming Chen distribution as a baseline model. In this dynamic system, failure of a component induces a higher load on the surviving components and thus increases component hazard rate through a power‐trend process. The classical and Bayesian point estimates of the unknown parameters of the composite system are obtained by the method of maximum likelihood and Markov chain Monte Carlo techniques, respectively. In the Bayesian framework, we have used gamma priors to obtain Bayes estimates of unknown parameters under the squared error and generalized entropy loss functions. The interval estimates of the baseline reliability function are obtained by using the Fisher information matrix and Bayesian method. A parametric hypothesis test is presented to test whether the failed components change the hazard rate function. A compact simulation study is carried out to examine the behavior of the proposed estimation methods. Finally, one real data analysis is performed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this article, maximum deviations of sample autocovariances and autocorrelations from their theoretical counterparts over an increasing set of lags are considered. The asymptotic distribution of such statistics for physically dependent stationary time series, which is of Gumbel type, only depends on second‐order properties of the underlying time series. Since the autoregressive sieve bootstrap is able to mimic the second‐order structure asymptotically correctly it is an obvious problem whether the autoregressive (AR) sieve bootstrap, which has been shown to work for a number of relevant statistics in time series analysis, asymptotically works for maximum deviations of autocovariances and autocorrelations as well. This article shows that the question can be answered positively. Moreover, potential applications including spectral density estimation and an investigation of finite sample properties of the AR‐sieve bootstrap proposal by simulation are given. [ABSTRACT FROM AUTHOR]

This paper presents a worst case approach for robust geometry and topology optimization of plane frames with global stability constraint. Uncertainty is assumed to exist in the nodal locations and cross‐sectional areas, and the worst values of the objective and stability constraint functions are relaxed to the quantile structural responses represented by the order statistics with given robustness and confidence levels. In order to alleviate the difficulty caused by melting nodes to some extent, the force density method is applied to an auxiliary truss model for geometry optimization of the frame, and the closely spaced nodes are merged. A method is presented for generating correlated imperfections for the nodal locations along each member, and a penalization approach is proposed for geometrical stiffness matrix to exclude superficial local buckling. It is demonstrated in the numerical examples that the result of robust optimization obtained by the proposed method is less sensitive to the uncertainty, and the stability constraint is also satisfied under uncertainty with the specified robustness and confidence levels. [ABSTRACT FROM AUTHOR]

Multipath interference commonly exists in wireless communication, navigation and radar systems, which may cause severe signal fading and bit error rate (BER) performance degradation. Therefore the detection of multipath interference is urgently needed. This paper proposes a high order statistics (HOS) based multipath interference detection method, since the HOS of the received signal show distinct difference when multipath interference exists. Moreover, the generalized theoretical values of the moments and cumulants, which release the demand for prior knowledge of timing information and symbol period, are deduced in this paper. It makes the proposed HOS features based detection method robust in blind environment. Computer simulations are performed to verify the proposed method. [ABSTRACT FROM AUTHOR]

Bollobás‐Riordan random pairing model of a preferential attachment graph Gmn is studied. Let {Wj}j ≤ mn + 1 be the process of sums of independent exponentials with mean 1. We prove that the degrees of the first νmn≔nmm+2−ε vertices are jointly, and uniformly, asymptotic to {2(mn)1/2(Wmj1/2−Wm(j−1)1/2)}j∈[νmn], and that with high probability (whp) the smallest of these degrees is nε(m+2)2m, at least. Next we bound the probability that there exists a pair of large vertex sets without connecting edges, and apply the bound to several special cases. We propose to measure an influence of a vertex v by the size of a maximal recursive tree (max‐tree) rooted at v. We show that whp the set of the first νmn vertices does not contain a max‐tree, and the largest max‐tree has size of order n. We prove that, for m > 1, ℙ(Gmnis connected)≥1−O((logn)−(m−1)/3+o(1)). We show that the distribution of scaled size of a generic max‐tree in G1n converges to a mixture of two beta distributions. [ABSTRACT FROM AUTHOR]

Risk measures, such as value‐at‐risk and expected shortfall, are widely used in finance. With the necessary sample size being computed using asymptotic expansions for relative errors, we propose a general framework to simulate these risk measures for a wide class of dependent data. The asymptotic expansions are new even for independent and identical data. An extensive numerical study is conducted to compare the proposed algorithm against existing algorithms, showing that the new algorithm is easy to implement, fast and accurate, even at the 0.001 quantile level. Applications to the estimation of intra‐horizon risk and to a comparison of the relative errors of value‐at‐risk and expected shortfall are also given. [ABSTRACT FROM AUTHOR]

Many variables encountered in practice have skewed distributions. While the sample mean is unbiased for the true mean regardless of the underlying distribution that generated the sample observations, it can be highly unstable in the context of skewed distributions. To cope with this problem, we propose an efficient estimator of the population mean based on the concept of conditional bias of a unit, which can be viewed as a measure of its influence. The idea is to reduce the impact of the sample units that have a large influence. The resulting estimator depends on a cut‐off value. We suggest selecting the cut‐off value that minimizes the maximum absolute estimated conditional bias with respect to the proposed estimator. An estimator of the mean square error is also presented. An empirical investigation comparing several estimators in terms of relative bias and relative efficiency suggests that the proposed estimator and the estimator of its mean square error perform well for a wide class of distributions. [ABSTRACT FROM AUTHOR]

Summary: We connect copula properties with stochastic comparisons between order statistics (k‐out‐of‐n systems) and coherent systems with dependent components. The copula dependence properties lead to marginal distribution‐free ordering properties between systems. Conversely, ordering properties of systems lead to properties (or new proofs of properties) for the baseline copulas. These relationships can be used to explain the meaning of mathematical properties and/or functional inequalities arising in the class of copulas. Some illustrative examples are provided including series and parallel systems with two or three components. The procedure introduced here can be applied to various system structures, even in high dimensions. In practice they can be used to determine various facets of dependency among the components of a system. [ABSTRACT FROM AUTHOR]

Functional data are commonly observed in many emerging biomedical fields and their analysis is an exciting developing area in statistics. Numerous statistical methods, such as principal components, analysis of variance, and linear regression, have been extended to functional data. The statistical analysis of functions can be significantly improved using nonparametric and robust estimators. New ideas of depth for functional data have been proposed in recent years and can be extended to image data. They provide a way of ordering curves or images from center‐outward, and of defining robust order statistics in a functional context. In this paper we develop depth‐based global envelope tests for comparing two groups of functions or images. In addition to providing global P‐values, the proposed envelope test can be displayed graphically and indicates the specific portion(s) of the functional data (eg, in pixels or in time) that may have led to rejection of the null hypothesis. We show in a simulation study the performance of the envelope test in terms of empirical power and size in different scenarios. The proposed depth‐based global approach has good power even for small differences and is robust to outliers. The methodology introduced is applied to test whether children with normal and low birth weight have similar growth pattern. We also analyzed a brain image dataset consisting of positron emission tomography scans of severe depressed patients and healthy controls. The global envelope test was used to find and visualize differences between the two groups. [ABSTRACT FROM AUTHOR]

Summary: We propose an efficient estimation method for the income Pareto exponent when only certain top income shares are observable. Our estimator is based on the asymptotic theory of weighted sums of order statistics and the efficient minimum distance estimator. Simulations show that our estimator has excellent finite‐sample properties. We apply our estimation method to US top income share data and find that the Pareto exponent has been ranging between 1.4 and 1.8 since 1985, suggesting that the rise in inequality during the last three decades is mainly driven by redistribution between the rich and poor, not among the rich. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a new robust auto‐adaptive approach for pseudo‐noise (PN) code acquisition is proposed. It is applied to the generalized multi‐carrier direct‐sequence code‐division multiple‐access (MC DS‐CDMA) systems communicating over frequency‐selective multipath Rayleigh fading channels. This new approach is based on the constant false alarm rate (CFAR) detection algorithm, referred here as automatic selection partial sum ordered statistics (ASPSOS)‐CFAR. The proposed approach does not require any prior information about the background environment and uses maximum likelihood estimation (MLE) method to detect the interfering signals group in the ranked cells for the full reference window. Once this group is identified and censored, the remaining smaller ranked cells are combined to form an estimate of the background noise level to compute the adaptive threshold. Through simulations, the performance of the proposed detector is analyzed and compared with traditional CFAR detectors based on fixed or automatic censoring algorithms. The obtained results show that the proposed detector eliminates the drawbacks of the previously related detectors and offers a robust detection performance to enhance the acquisition process in heterogeneous background environments. [ABSTRACT FROM AUTHOR]

After the completion of many studies, experimental results are reported in terms of distribution‐free confidence intervals that may involve pairs of order statistics. This article considers a meta‐analysis procedure to combine these confidence intervals from independent studies to estimate or construct a confidence interval for the true quantile of the population distribution. Data synthesis is made under both fixed‐effect and random‐effect meta‐analysis models. We show that mean square error (MSE) of the combined quantile estimator is considerably smaller than that of the best individual quantile estimator. We also show that the coverage probability of the meta‐analysis confidence interval is quite close to the nominal confidence level. The random‐effect meta‐analysis model yields a better coverage probability and smaller MSE than the fixed‐effect meta‐analysis model. The meta‐analysis method is then used to synthesize medians of patient delays in pulmonary tuberculosis diagnosis in China to provide an illustration of the proposed methodology. [ABSTRACT FROM AUTHOR]

Quantiles are widely used in both theoretical and applied statistics, and it is important to be able to deploy appropriate quantile estimators. To improve performance in the lower and upper quantiles, especially with small sample sizes, a new quantile estimator is introduced which is a weighted average of all order statistics. The new estimator, denoted NO, has desirable asymptotic properties. Moreover, it offers practical advantages over four estimators in terms of efficiency in most experimental settings. The Harrell–Davis quantile estimator, the default quantile estimator of the R programming language, the Sfakianakis–Verginis SV2 quantile estimator and a kernel quantile estimator. The NO quantile estimator is also utilized in comparing two independent groups with a percentile bootstrap method and, as expected, it is more successful than other estimators in controlling Type I error rates. [ABSTRACT FROM AUTHOR]

Summary: Four calibration algorithms based on the order statistics about capacitive mismatch are proposed for successive approximation register (SAR) analog‐to‐digital converter (ADC). An 18‐bit split capacitive SAR ADC architecture with redundant bits was used to verify the four calibration algorithms proposed. The main dynamic parameters of the SAR ADC were simulated in MATLAB by 500 Monte‐Carlo runs with a standard deviation of 0.1% (σ0/C0 = 0.001). And the simulation results of sorting and regrouping method II (SRGII) show that a 21.64‐dB enhancement of spurious‐free dynamic range (SFDR) and a 3.33‐bit improvement of effective number of bits (ENOB) have achieved respectively, whereas the simulation results of sorting and re‐exchanging method I (SREI) show that a 21.64‐dB enhancement of SFDR and a 3.34‐bit improvement of ENOB have achieved, respectively [ABSTRACT FROM AUTHOR]

There has been considerable interest in recent years in quantifying the rate of unavoidable or so-called random cancers, as opposed to cancers linked to environmental, genetic or other factors. We propose a data-based approach to estimate an upper limit to this probability, based on an analysis of multiple registry data. The argument is that the cumulative hazards for random cancers cannot exceed the minimum reliable cumulative hazard observed across the registries. We propose a Monte Carlo method to identify this upper limit and apply the method to data on nine different cancers recorded by 423 registries. We compare our values with estimates obtained from a random mutations argument. [ABSTRACT FROM AUTHOR]

We study the use of ranked set sampling (RSS) with binary outcomes in cluster‐randomized designs (CRDs), where a generalized linear mixed model (GLMM) is used to model the hierarchical data structure involved. Under the GLMM‐based framework, we propose three different approaches to estimate the treatment effect, including the nonparametric (NP), maximum likelihood (ML) and pseudo likelihood (PL) estimators. We investigate their asymptotic properties and examine their finite‐sample performance via simulation. Based on these three RSS estimators, we further develop procedures for testing the existence of the treatment effect. We examine the power and size of our proposed RSS tests and compare them with existing tests based on simple random sampling (SRS). All the proposed RSS estimation and test methods are illustrated with two data examples, one for rare events and the other for non‐extreme events. Throughout our investigations, we also consider the possible effect of imperfect ranking. Among the proposed methods, we provide recommendations on whether to use RSS rather than SRS with binary outcomes in CRDs and, if yes, when to use which RSS method. The Canadian Journal of Statistics 48: 342–365; 2020 © 2019 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Summary: Basically, nonorthogonal multiple access (NOMA) allows controllable interferences by nonorthogonal resource allocation with a tolerable increase in receiver complexity, using successive interference cancellation (SIC). In this paper, authors show a novel mathematical model of teletraffic for users accessing, simultaneously, to Wi‐Fi and LTE services by using NOMA, calculating the birth–death process by order statistics. This methodology has not been previously used. The mathematical model is represented by a two‐dimensional Markovian process where the users can born or die in one system or another, independently, and results are validated through simulations. The outcomes demonstrate an increment of the sum‐rate gain for a system where users are ordered in the power domain using order statistics, according to the signal interference plus noise ratio (SINR), compared to a system where these statistics are not employed. By using the proposed mathematical model, the sum‐rate gain increases around 15%, and it is also demonstrated that this algorithm foresees a steady behavior of the sum rate, even when the number of channels is augmented, contrary when no order statistics are employed, in which the sum rate decreases considerably. On the other hand, the blocking probability is also demonstrated based on the chance of moving from one technology to another. [ABSTRACT FROM AUTHOR]

Summary: In a multicarrier continuous‐variable quantum key distribution (CVQKD) protocol, the information is granulated into Gaussian subcarrier CVs and the physical Gaussian link is divided into Gaussian sub‐channels. Here, we propose a combined mathematical framework of order statistics and random matrix theory for multicarrier continuous‐variable quantum key distribution. The analysis covers the study of the distribution of the sub‐channel transmittance coefficients in the presence of a Gaussian noise and the utilization of the moment generation function (MGF) in the error analysis. We reveal the mathematical formalism of sub‐channel selection and formulation of the transmittance coefficients and show a reduced complexity progressive sub‐channel scanning method. We define a framework to evaluate the statistical properties of the information flowing processes in multicarrier CVQKD protocols. Using random matrix theory, we express the achievable secret key rates and study the efficiency of the adaptive multicarrier quadrature division‐multiuser quadrature allocation (AMQD‐MQA) multiple‐access multicarrier CVQKD. The proposed combined framework is particularly convenient for the characterization of the physical processes of experimental multicarrier CVQKD. [ABSTRACT FROM AUTHOR]