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The 2022 International Symposium on Nonparametric Statistics was held in Paphos, Cyprus and co-sponsored by the Institute of Mathematical Statistics and the Bernoulli Society of Mathematical Statistics and Probability. The symposium brought together researchers from around the world to discuss recent advances and trends in nonparametric statistics. The conference covered a wide range of topics, including nonparametric estimation, hypothesis testing, adaptive inference, high-dimensional statistical inference, and more. The special issue of the Journal of Nonparametric Statistics contains papers that have undergone a peer review process and cover diverse areas of nonparametric statistics. [Extracted from the article]

Note, for instance, that the probabilities given by Castellares et al. ([1]) in page 4 are the same than those shown in expression (9.115) in the book by Johnson et al. ([3]), with the change of parameters Graph HT ht and Graph HT ht Neyman type A (NTA) distribution is frequently used in Biology, Biodosimetry, Environmental Sciences, Epidemiology, etc. A count random variable I X i is said to follow a stopped-sum Poisson, compound Poisson, multiple Poisson or clustered-Poisson distribution, if it can be represented as Graph HT ht where I N i is a Poisson random variable with parameter Graph HT ht and Graph HT ht are independent, identically distributed random variables that are also independent of I N i . [Extracted from the article]

The global Covid-19 pandemic has passed. This process required greater attention and care to the specifics of the organization of distance learning and the resolution of problems that arose for participants in the educational process. By late 2021 face-to-face teaching was returning but Russian aggression against Ukraine interrupted the comparatively carefree life of children and hindered access to kindergartens and schools which required a further focus on remote education. The paper outlines the peculiarities of the organization of distance learning under martial law in Ukraine and presents the problems of the organization of training during a time of conflict as well as the challenges presented by Internet platforms for the organization of the distance learning approaches recommended by the Ministry of Education of Ukraine. The aim of the research was theoretical analysis and generalization of literature on research problems, pedagogical observations, surveys, methods of mathematical statistics. The article provides one of the first analyses of the difficulties faced during this period of immense disruption based on empirical data and explains to what extent Ukrainian teachers under martial law have the possibility to organize distance teaching, what problems they face, what is the psychological state of children. [ABSTRACT FROM AUTHOR]

In order to improve the effect of agricultural economic structure optimisation, this paper builds an agricultural economic structure optimisation analysis system based on factor analysis and intelligent algorithms, and uses a set of low-dimensional hidden factor vectors to describe the covariance matrix structure of high-dimensional observation vectors. Moreover, this paper combines the algorithm with the actual situation to obtain the optimisation analysis process of the agricultural economic structure. On this basis, this paper analyses the optimisation of agricultural economic structure in practice with a case analysis method. Moreover, this paper uses mathematical analysis to process agricultural economic structure data, and uses mathematical statistics to visualise the process of data processing. In addition, this paper combines the weighted average to perform parameter processing, combines with the comparative analysis method to obtain the agricultural economic results parameters, and analyses these parameters. Finally, on the basis of the above, this paper proposes the corresponding optimisation strategy of agricultural economic structure. The research results show that the method proposed in this paper has a certain effect. [ABSTRACT FROM AUTHOR]

Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability calculations and allowing important developments in probability theory. However, can this result be proven without advanced elements from probability theory, such as independent σ-fields and related results? This paper aims primarily to fill this possible gap. Two elementary proofs that require only introductory probability content are given in detail and compared with the 'technical' proof found in books on advanced probability theory. A discussion regarding how these proofs could be included in regular probability courses is also included in the survey. [ABSTRACT FROM AUTHOR]

In 'Many-valued Logics', a lecture broadcast over New Zealand's public radio in 1957, Arthur N. Prior (1914–1969) complained that conjunctions are put 'to something like forced labour' in Łukasiewicz's three-valued semantics, Ł3. In this paper, we discuss what Prior might have meant by this. [ABSTRACT FROM AUTHOR]

This study aimed to determine how watching lecture videos at 1× and 2× speeds affects memory retention in medical students. A posttest-only experimental design was utilized. The participants were 60 Year-1 and Year-2 medical students. The participants were assigned to one of two groups through stratified randomization: Group 1 would watch the video at 1× speed, and Group 2 at 2× speed. Their performance was assessed using a test comprising 20 multiple-choice questions. The test has been applied immediately after watching the video (Immediate test), and, again after one week (Delayed test). Parametric and non-parametric statistical tests were performed. In the Immediate test, the mean score of the 1× speed group was 11.26 ± 4.06, while 2× speed group's mean score was 10.16 ± 2.46. The difference was not significant t(58) = 1.26, p >.05. In the Delayed test, the mean score of 1× speed group was 9.66 ± 3.94, while 2× speed group's mean score was 8.36 ± 2.80. The difference was not significant t(55) = 1.42, p >.05. Watching the video lecture at 2× speed did not impair memory retention in medical students. This may help students to save time in their dense curricula. Practice points Many medical students watch lecture videos at 2× (double) speed to save time. While this is a time-saver, the negative impact on their learning is unclear. This paper describes a randomized trial that measures the learning impact when medical students watch an instructional video at 2× speed and finds that there is no significant negative impact on their learning. [ABSTRACT FROM AUTHOR]

Persuasive gamified systems are effective tools for motivating behaviour change using various persuasive strategies. In line with the reinforcement theory, some persuasive gamified systems employ reward and punishment in their design to achieve the intended behavioural outcome. Research has argued both in favour and against using these strategies in behaviour change applications due to mixed results with respect to their effectiveness. However, there is a lack knowledge about how interventions using these strategies could motivate or demotivate behaviours. Therefore, this paper explores the mechanism through which Reward and Punishment motivate or demotivate behaviours with respect to their strengths and weaknesses. The results of large-scale exploratory studies (N = 1768) uncover important strengths and weaknesses that could facilitate or hinder the effectiveness of Reward and Punishment at motivating behaviour change. These include their ability to engage users and make behaviour fun, reinforce commitments to goals, and reveal some consequences of bad behaviour. We also compared the perceived effectiveness of reward and punishment quantitatively. [ABSTRACT FROM AUTHOR]

Effective teaching of concepts related to human computer interaction (HCI) requires introduction of the core paradigms as well as the design and evaluation methodologies to the learners. In this paper, we investigate the learning effectiveness of a tool-mediated learning activity to support instruction of established human performance models, namely the Keystroke Level Model (KLM) and Fitts' law, and their application in web form design practice. The tool, named Keystroke Level Model Form Analyser (KLM-FA), supports learning through exploration by providing step-by-step tracing of the KLM modelling for any web form filling task. KLM-FA can be used in modelling exercises of either online or offline web forms according to different interaction strategies or users' characteristics. Three pretest-posttest studies involving 52 students in total enrolled in computer science curricula with different education delivery methods (campus-based, blended learning, distance learning) and levels (undergraduate, postgraduate) provide evidence for the effectiveness of the proposed learning activity. In all three studies, it was found that the KLM-FA activity had a significant positive effect on students' learning gain. In addition, students rated their perceived educational experience and KLM-FA usability as rather high. Content analysis of students' comments also found that KLM-FA is an educationally valuable and usable tool. [ABSTRACT FROM AUTHOR]

This paper presents a universal model of weighted coordinate transformation, i.e. transformation considering the errors of coordinates in both coordinate systems. It is intrinsically one of the typical examples of ‘error-in-variables’ (EIV) models. The proposed method of LS theory application on weighted coordinate transformation does not impose any constraints on the form of functional relationship among stochastic variables. Since the basic idea is to generalise Gauss–Markov model (GMM) by introduction of so-called ‘total residuals’, the proposed procedure is named ‘Generalised Gauss–Markov model’. Formulation of expressions for estimation of unknown transformation parameters is theoretically confirmed using the Gauss–Helmert model (GHM) and three different modifications of the GMM. The proposed procedure is in its essence a strict solution to total least-squares (unweighted) and weighted total least-squares problem in coordinate transformation. This thesis is experimentally confirmed by comparison of its results with those found in four characteristic examples from the literature. [ABSTRACT FROM AUTHOR]

The paper by Johnson [Systems of frequency curves generated by the methods of translation, Biometrika 36 (2014), pp. 149-176] has introduced a very interesting univariate distribution with bounded support which is known in the statistical literature as the class of distributions. In this paper we generalize this class of univariate distributions to the multivariate case whose marginals are distributions. On the basis of the multivariate distribution introduced, we propose a multivariate regression model for dealing with multivariate response variables which are vectors of rates or proportions. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. Monte Carlo simulation results reveal that the maximum likelihood method can be used effectively in estimating the model parameters. An application to real data is presented to show the usefulness of the multivariate regression model in practice. [ABSTRACT FROM AUTHOR]

In this paper, we study the steady state behaviour of an M/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server's breakdowns occurring randomly at any instant while serving the customers and delayed repair. We assume that customers arrive to the system according to a Poisson process with rate 'λ' and the server provides two types of general heterogeneous service. At the beginning of a service, a customer has the option to choose any one type of service. After completion of either type of service, the customer has the further option to repeat the same type of service. For this model, we first derive the joint distribution of state of the server and queue size by considering both elapsed and remaining time, which is one of the objectives of this paper. Secondly, we derive the probability generating function of the stationary queue size distribution at departure epoch. Next, we derive Laplace-Stieltjes transform of busy period distribution and waiting time distribution. Finally, we obtain some important performance measure and reliability indices of this model. [ABSTRACT FROM AUTHOR]

In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a semiparametric estimation procedure that first estimates the mean of the underlying normal distribution and then recovers non-parametrically the density of the corresponding mixing distribution. We illustrate the performance of our procedure on simulated and real data. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following simple linear errors-in-variables regression model:where θ and β are the unknown parameters, ηi, ξi’s are observable andxi’s are unobservable. We assume the error variables {(ε1, δi), 1≤i≤n} form aL2stationary α-mixing sequences. In this paper, we obtained the moderate deviation principles for the least-square estimators of the unknown parameters θ and β. [ABSTRACT FROM AUTHOR]

Maji et al. [Robust statistical inference based on the C-divergence family. Ann Inst Stat Math. 2019;71:1289–1322] introduced the minimum C-divergence estimators and plugging them in the C-divergence measures give test statistics for testing simple null and composite null hypotheses. One inconvenience of these test statistics is that their asymptotic distribution is not, in general, a chi-square distribution but a linear combination of chi-square distributions. To overcome this inconvenience, in this paper we consider Wald-type test statistics based on minimum C-divergence estimators. We establish that this family of test statistics is a chi-square distribution and we get an approximation of the power function under simple null hypothesis and composite null hypothesis. We have calculated both first order and second order influence function of the Wald-type test statistics and based on it we can see the robustness of the family of test statistics considered in this paper. Both simulated and real data examples have been shown as part of numerical results. [ABSTRACT FROM AUTHOR]

Understanding the flow pressure distribution on the blade airfoil of the tidal turbine is of great significance for optimising the energy harvesting performance of the blades. In this paper, a bidirectional type horizontal tidal turbine (BHTT) with special S-shaped blades is proposed, which have a larger pitch diameter ratio provide excellent performance at low oncoming flow velocity by the theoretical, numerical and experimental methods. First, it is verified that the energy harvesting efficiency is basically the same in the case of bidirectional flow, and the S-shaped blade is divided into multiple slice sections, which could quantify the energy harvesting performance of each area of the blade. Then, using the method of mathematical statistics to divide more areas, the probability density shows a skewed distribution. The results show that the energy harvesting performance is less affected by flow velocity fluctuation, and the energy harvesting efficiency could reach 0.25-0.55 when the tip speed ratio is in the range of 0.2-0.5. Furthermore, the slice section method is adopted to make the influence of axial thrust intuitive and clear to study the turbine energy harvesting performance and improve the harvesting efficiency, which could provide a reference for the engineering design of tidal turbines. [ABSTRACT FROM AUTHOR]

In this paper, we consider a measure of inaccuracy between distributions of the nth record value and parent random variable. We also propose the measure of residual inaccuracy of record values and study characterization results of dynamic cumulative residual inaccuracy measure. We discuss some properties of the proposed measures. [ABSTRACT FROM AUTHOR]

In this paper, an up-to-date overview is provided on the data driven-based fault diagnosis (FD) and remaining useful life (RUL) prediction problems of the petroleum machinery and equipment (PME). First, the FD and RUL prediction of five key components including bearings, gears, motors, pumps and pipelines are discussed by adopting mathematical statistics and shallow learning. Then, four kinds of widely-used DL models, i.e. deep neural networks, deep belief networks, convolution neural networks and recurrent neural networks, are surveyed, and the applications in the field of PME are highlighted. Finally, the possible challenges are proposed and some corresponding research directions in the future are presented. [ABSTRACT FROM AUTHOR]

Most research on 3D model retrieval focus on shape as the main feature used for search and retrieval. In this paper, we explore augmenting 3D shape-based similarity measures by combining shape with color features. There are already numerous techniques for content-based 3D model retrieval utilizing shape, some use global shape features, shape distributions, or view-based methods. This paper uses a view-based approach using 2D projections of 3D models taken from different viewpoints. The main problem with view-based techniques is how to normalize the rotation of the mesh in 3D space to properly align the model to the projection planes. In our work, we use Normal-vectors PCA (NPCA). The 3D model is first projected onto three planes using their normal vectors and gray-level images (inner elevations) that describe the depth information are generated. The angular radial transform (ART) from MPEG-7 is then used on these inner elevations to extract a feature descriptor. These descriptors are called the inner elevation descriptor (IED) and are used to match the query with the database object. This shape feature is then augmented using color histograms considering perceptual color similarity. It is then tested on the Princeton Shape Benchmark and compared to well-known approaches. [ABSTRACT FROM AUTHOR]

LetXandbe independent and identically distributed random variables withEX=0, and setSn=∑k≤nXk,Vn=√∑k≤nXk2,. In this paper, we derive, under some mild conditions, precise asymptotics for ∑n((log |n|)b/|n|(log |n|)d−1)E{(|Sn|/Vn)−ϵ√log |n|}+as ϵ↘ 0. [ABSTRACT FROM AUTHOR]

The score statisticS2is commonly used for general likelihood-based inference. Pearson’s Chi-squared statisticX2= ∑(O−E)2/Eis ubiquitous in contingency table inference. Because tests and confidence intervals based onS2have been shown to work well in practice and theory and becauseX2has such a simple and intuitively appealing form, it is of interest to know whenS2is identical toX2and whenX2has an approximate Chi-squared distribution. Toward these ends, this paper gives a simple proof thatS2=X2for the broad class of multinomial-Poisson distributions when the alternative hypothesis is unrestricted in a certain sense. This paper also gives a sufficient condition under which the null distribution of the Pearson score statistic is approximately Chi-squared. Several examples illustrate the utility of the results and counter-examples highlight the importance of the sufficient conditions of the results. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for sampling items that are checked on a pass/fail basis, with a view to a statement being made about the success/ failure rate for the purposes of promoting an organisation's product/service to potential clients/customers. Attention is paid to the appropriate use of statistical phrases for the statements and this leads to the use of Bayesian credible intervals, thus it exceeds what can be achieved with standard acceptance sampling techniques. The hypergeometric distribution is used to calculate successive stopping rules so that the resources used for sampling can be minimised. Extensions to the sampling procedure are considered to allow the potential for stronger and weaker statements to be made as sampling progresses. The relationship between the true error rate and the probabilities of making correct statements is discussed. [ABSTRACT FROM AUTHOR]

In this paper, some complete convergence and complete moment convergence results for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are studied. The obtained theorems not only extend the result of Gan and Chen (2007) to the case of NSD random variables, but also improve them. [ABSTRACT FROM AUTHOR]

Testing the predictive performance of energy models (EMs) is necessary to evaluate their accuracies. This paper investigates the adequacy of existing statistical metrics that are often used by professionals and researchers to test EMs. It discerns that coefficient of variance of root mean squared error (CVRMSE) and mean bias error (MBE), which are prescribed in ASHRAE guideline 14, are not suitable for system-level energy model testing. It points out the limitations of CVRMSE, MBE, and also root mean squared error (RMSE). The analysis shows that the normalizing term of statistical metrics influences its accuracy in determining the predictive performance of EMs. An alternative metric (range normalized root mean squared error, RN_RMSE) is proposed that normalizes the RMSE by the range of the data as a replacement for CVRMSE. It is shown that RN_RMSE when used in tandem with can provide more meaningful and accurate representation of the performance of system-level EMs. Abbreviations Ems: energy models; IDFs: input data files; R2: coefficient of determination; RMSE: root mean squared error; CVRMSE: coefficient of variance of root mean squared error; MBE: mean bias error; RN RMSE: range normalized root mean squared error [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the complete moment convergence of double-indexed randomly weighted sums of negatively superadditive-dependent (NSD, for short) random variables, which is stronger than complete convergence. In addition, the convergence of double-indexed randomly weighted sums of NSD random variables is also obtained. As applications, we obtain the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors, and study the almost sure convergence and mean square convergence of the state observers of linear-time-invariant systems. [ABSTRACT FROM AUTHOR]

For any fixed integer , let be real-valued random variables with a common subexponential distribution, and let be positive random variables which are bounded above and independent of . Under some rather loose conditional dependence assumptions on the primary random variables , this paper proves that the asymptotic relationshold as , where are arbitrarily dependent. In particular, it is shown that the above results hold true for with certain Samarnov distributions. The obtained results on randomly weighted sums are applied to estimating the finite-time ruin probability in a discrete-time risk model with both insurance and financial risks. [ABSTRACT FROM AUTHOR]

The smoothing spline method is used to fit a curve to a noisy data set, where selection of the smoothing parameter is essential. An adaptiveCpcriterion (Chen and Huang 2011) based on the Stein’s unbiased risk estimate has been proposed to select the smoothing parameter, which not only considers the usual effective degrees of freedom but also takes into account the selection variability. The resulting fitted curve has been shown to be superior and more stable than commonly used selection criteria and possesses the same asymptotic optimality asCp. In this paper, we further discuss some characteristics on the selection of smoothing parameter, especially for the selection variability. [ABSTRACT FROM PUBLISHER]

There hides a certain relationship among various monitoring data in a landslide, and the mining of this relationship is of significance to landslide research. In this paper, we first collect multiple monitoring data of riverside 1# slump-mass of Huangtupo landslide, the Three Gorges Reservoir Region, China, including Global Positioning System (GPS) monitoring data, inclinometer data, reservoir water level, rainfall, water content, crack width, groundwater level and temperature data, etc. By adopting the combination of quantitative statistics and qualitative simulation method for multi-sensor fusion monitoring data analysis, we overcome the one-sidedness of using a single method or single data type. The result of fusion analysis has indicated that in time periods with low rainfall or when the rainfall is not the major factor, main factors affecting landslide movement are crack development, water content of the landslide and water level of the Three Gorges Reservoir. Compared with the actual monitoring data, the fusion analysis results has a maximum error of 1.9%, which shows a good effect. [ABSTRACT FROM AUTHOR]

The modular estimates for the fractional integral operators and thek-plane transforms are obtained in this paper. These estimates are obtained by using the modular estimates of Hardy operators and the modular interpolation theorem. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to propose a revision of the well-known Campbellian system for causal research. The revised system, termed the COPS model, applies to both applied and basic research. Five validities are included, where two validities are adopted from the Campbellian system, and the validities are partly hierarchically ordered. Important similarities and differences between the Campbellian system and the COPS model are discussed. [ABSTRACT FROM AUTHOR]

Seamless phase II/III clinical trials have attracted increasing attention recently. They mainly use Bayesian response adaptive randomization (RAR) designs. There has been little research into seamless clinical trials using frequentist RAR designs because of the difficulty in performing valid statistical inference following this procedure. The well-designed frequentist RAR designs can target theoretically optimal allocation proportions, and they have explicit asymptotic results. In this paper, we study the asymptotic properties of frequentist RAR designs with adjusted target allocation proportions, and investigate statistical inference for this procedure. The properties of the proposed design provide an important theoretical foundation for advanced seamless clinical trials. Our numerical studies demonstrate that the design is ethical and efficient. [ABSTRACT FROM AUTHOR]

An outlier is defined as an observation that is significantly different from the others in its dataset. In high-dimensional regression analysis, datasets often contain a portion of outliers. It is important to identify and eliminate the outliers for fitting a model to a dataset. In this paper, a novel outlier detection method is proposed for high-dimensional regression problems. The leave-one-out idea is utilized to construct a novel outlier detection measure based on distance correlation, and then an outlier detection procedure is proposed. The proposed method enjoys several advantages. First, the outlier detection measure can be simply calculated, and the detection procedure works efficiently even for high-dimensional regression data. Moreover, it can deal with a general regression, which does not require specification of a linear regression model. Finally, simulation studies show that the proposed method behaves well for detecting outliers in high-dimensional regression model and performs better than some other competing methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the precise large deviations for sums of φ-mixing and UND random variables with long-tailed distributions. The asymptotic relations for non random sum and random sum of random variables with long-tailed distributions are obtained. [ABSTRACT FROM AUTHOR]

In this paper, polynomially-based discrete M-Galerkin and M-collocation methods are proposed to solve nonlinear Fredholm integral equation with a smooth kernel. Using sufficiently accurate numerical quadrature rule, we establish superconvergence results for the approximate and iterated approximate solutions of discrete Legendre M-Galerkin and M-collocation methods in both infinity and L2-norm. Numerical examples are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

For testing the independence of two vectors with respective dimensionsand, the existing literature in high-dimensional statistics all assume that both dimensionsandgrow to infinity with the sample size. However, as evidenced in RNA-sequencing data analysis, it happens frequently that one of the dimension is quite small and the other quite large compared to the sample size. In this paper, we address this new asymptotic framework for the independence test. A new test procedure is introduced and its asymptotic normality is established when the vectors are normally distributed. A Monte-Carlo study demonstrates the consistency of the procedure and exhibits its superiority over some existing high-dimensional procedures. It is also shown that the procedure is robust against the normality assumption on the population vectors. Applied to a set of RNA-sequencing data, we obtain very convincing results on pairwise independence/dependence of gene isoform expressions as attested by prior knowledge established in that field. [ABSTRACT FROM AUTHOR]

This paper deals with computing shortest width tolerance intervals controlling both tails of the exponential distribution on the basis of record values. Equal-tailed and shortest tolerance factors are derived. The expected widths of these tolerance intervals are evaluated via a Monte Carlo simulation study. Finally, two illustrative examples are also included. [ABSTRACT FROM PUBLISHER]

In this paper, we study the complete convergence and complete moment convergence for negatively orthant-dependent random variables. Especially, we obtain the Hsu–Robbins-type theorem for negatively orthant-dependent random variables. Our results generalize the corresponding ones for independent random variables. [ABSTRACT FROM AUTHOR]

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes. [ABSTRACT FROM AUTHOR]

Standard meta-analysis requires the quantity of interest and its estimated variance to be reported for each study. Datasets that lack such variance information pose important challenges to meta-analytic inference. In a study with continuous outcomes, only sample means and sample sizes may be reported in the treatment arm. Classical meta-analytical technique is unable to apply statistical inference to such datasets. In this paper, we propose a statistical tool for testing equal means between two groups in meta-analysis when the variances of the constituent studies are unreported, using pivot inference based on the exact t-distribution and the generalized likelihood ratio. These are considered under a fixed-effect model. In simulations, the type I errors and power probabilities of the proposed tests are investigated as metrics of their performance. The t-test statistic provides type I errors very close to the nominal significance level in all cases and has large power. The generalized likelihood ratio test statistic performs well when the number of studies is moderate-to-large. The performance of our tests surpasses that of the conventional test, which is based on the normal distribution. The difference is especially pronounced when the number of studies is small. The distribution given by our tests is also shown to closely follow the theoretical distribution. [ABSTRACT FROM AUTHOR]

The paper presents the analysis of speech perception and of the specific nature of communication between migrants and residents of Moscow, as reflected in the digital environment. The main focus is on conflictogenic digital zones, as well as methods for predicting and preventing conflicts. The development of algorithms to make predictions about users' possible actions, the occurrence and prevention of conflicts is an important task of interdisciplinary research. The goals of research were achieved based on the analysis of social media data. Neural network modeling, statistical analysis, and differential equations were used as research methods. In mathematical modeling, three types of models were built: an equation of linear regression, as well as logistic and type-epidemiological mathematical models. The study showed that the use of parallel models using differential equations, mathematical statistics and neural network technology to determine the dynamics of aggressive online activity, in particular, to analyze users' perception of conflict situations related to the topic of migrants, makes it possible to correctly analyze conflict zones in the development of a modern metropolis, to increase the effectiveness of research methods and predictive analytics of the development of social tension. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed. [ABSTRACT FROM AUTHOR]

Markov kernels play a decisive role in probability and mathematical statistics theories, and are an extension of the concepts of σ -field and statistic. Concepts such as independence, sufficiency, completeness, ancillarity or conditional distribution have been extended previously to Markov kernels. In this paper, the concept of conditional expectation of a Markov kernel given another is introduced, setting its first properties. An application to clinical diagnosis is provided, obtaining an optimality property of the predictive values of a diagnosis test. In a statistical framework, this new probabilistic tool is used to extend to Markov kernels the theorems of Rao-Blackwell and Lehmann-Scheffé. A result about the completeness of a sufficient statistic is obtained in passing by properly enlarging the family of probabilities. As a final statistical scholium, a generalization of a result about the completeness of the family of nonrandomized estimators is given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the drift parameters estimation problem for the Vasicek-type model defined as d X t = a (b − X t) d t + d G t , X 0 = 0 , t ≥ 0 where a < 0 and b ∈ R are considered as unknown drift parameters and Gt is a self-similar Gaussian process with index L ∈ (1 / 2 , 1) . We provide sufficient conditions, based on the properties of G, ensuring the strong consistency and the asymptotic distributions of our estimators a ̂ of a and b ̂ of b based on the observation { X t } t ∈ [ 0 , T ] as T → ∞ . Our approach extend the result of Xiao and Yu (2017) for the case when G is a fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1) . We also discuss the cases of sub-fractional Browian motion and bi-fractional Brownian motion. The conclusion can also be extended to more general self-similarity processes, such as Hermite processes. [ABSTRACT FROM AUTHOR]

It is desirable to work efficiently and cost effectively to evaluate new therapies in a time-sensitive and ethical manner without compromising the integrity and validity of the development process. The seamless phase II/III clinical trial has been proposed to meet this need, and its efficient, ethical and economic advantages can be strengthened by its combination with innovative response adaptive randomization (RAR) procedures. In particular, well-designed frequentist RAR procedures can target theoretically optimal allocation proportions, and there are explicit asymptotic results. However, there has been little research into seamless phase II/III clinical trials with frequentist RAR because of the difficulty in performing valid statistical inference and controlling the type I error rate. In this paper, we propose the framework for a family of frequentist RAR designs for seamless phase II/III trials, derive the asymptotic distribution of the parameter estimators using martingale processes and offer solutions to control the type I error rate. The numerical studies demonstrate our theoretical findings and the advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

Consider a repairable system subject to shocks that arrive according to a non-homogeneous Poisson process (NHPP). As a shock occurs, two types of failure may be happened. Type-I failure occurs with probability q and is rectified by a minimal repair, whereas type-II failure takes place with probability p = 1−q and is removed by replacement. The system is replaced at the nth type I failure or at type II failure, whichever comes first. In the present paper, we find a general representation for the likelihood function of the proposed model. Then, we follow both classical and Bayesian procedures to estimate the model parameters when the time to first failure is a Weibull distribution. Because the Bayesian estimation cannot be obtained in a closed form, we use two approximation methods: Lindley's approximation and MCMC method. Finally, a Monte Carlo simulation is conducted to compare the performance of estimators in classical and Bayesian procedures. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying α-mixing triangular array of random variables. In particular, the uniformly boundedness assumption on the function class, which is required in most of the existing literature, is spared. Furthermore, under strict stationarity a weak convergence result for the sequential empirical process indexed in function classes is obtained as a direct consequence. Two examples in mathematical statistics, that cannot be treated with existing results, are given as possible applications. [ABSTRACT FROM AUTHOR]

This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces 'generalized inverted Kumaraswamy-G' family of distributions. We provide a comprehensive account of some of its mathematical properties that include the ordinary and incomplete moments, quantile and generating functions and order statistics. The infinite mixture representations for probability density and cumulative distribution and entropy functions of the new family are also established. The density function of the ith-order statistics is expressed as an infinite linear combination of baseline densities and model parameters are estimated by maximum likelihood method. Four special models of this family are also derived along with their respective hazard rate functions. The maximum likelihood estimation (MLE) method is used to obtain the model parameters. Monte Carlo simulation experiments are executed to assess the performance of the ML estimators under the corresponding generated models while some data applications are also illustrated. The results of the study show that the proposed distribution is more flexible as compared to the baseline model. This distribution especially can be used to model symmetric, left-skewed, right-skewed and reversed-J data sets. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. First, we investigate estimations in varying-coefficient partially linear errors-in-variables models with covariates missing at random. However, the estimators are often biased due to the existence of measurement errors, the bias-corrected profile least-squares estimator and local liner estimators for unknown parametric and coefficient functions are obtained based on inverse probability weighted method. The asymptotic properties of the proposed estimators both for the parameter and nonparametric parts are established. Second, we study asymptotic distributions of an empirical log-likelihood ratio statistic and maximum empirical likelihood estimator for the unknown parameter. Based on this, more accurate confidence regions of the unknown parameter can be constructed. The methods are examined through simulation studies and illustrated by a real data analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with the parameter estimation in partial linear model and we proposed a difference-based almost unbiased Liu estimator (DBAULE) for the vector ofβin partial linear model. Necessary and sufficient conditions for the DBAULE over the difference-based estimator and difference-based Liu estimator under the mean squared error sense are derived. Finally, a method is given to select the biasing parameter. A numerical example and a simulation study are given to explain the performance of the estimators. [ABSTRACT FROM PUBLISHER]