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We propose a robust post-selection inference method based on the Huber loss for the regression coefficients, when the error distribution is heavy-tailed and asymmetric in a high-dimensional linear model with an intercept term. The asymptotic properties of the resulting estimators are established under mild conditions. We also extend the proposed method to accommodate heteroscedasticity assuming the error terms are symmetric and other suitable conditions. Statistical tests for low-dimensional parameters or individual coefficient in the high-dimensional linear model are also studied. Simulation studies demonstrate desirable properties of the proposed method. An application to a genomic dataset about riboflavin production rate is provided.

A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a χ 2 distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as MCMC output) is available, the proposed statistic can be easily obtained as a by-product of posterior simulation. In addition, the numerical standard error of the estimated proposed statistic can be computed based on random samples. A robust version of the test statistic is developed under model misspecification and inherits many nice properties of the new posterior statistic. The finite sample performance of the statistics is examined in Monte Carlo studies. The method is applied to two latent variable models used in microeconometrics and financial econometrics.

We establish a feasible central limit theorem with convergence rate n 1 ∕ 8 for the estimation of the integrated volatility of volatility (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The central limit theorem is applied to provide interval estimates of the VoV and conduct hypothesis tests. Furthermore, when one is interested in the null hypothesis that the VoV is zero, we show that a more powerful test can be established based on a VoV estimator with a convergence rate n 1 ∕ 5 under the null. Empirical results on the S&P 500 and individual stocks show strong evidence of non-zero VoV.

It is a common practice to conduct principal component analysis (PCA) using standardized data, which is equivalent to applying PCA to the correlation matrix rather than the covariance matrix. Yet little research has been done about such differences in the context of high frequency data. This paper bridges this gap. We derive the analytical forms of the asymptotic biases and variances for the estimators of the integrated eigenvalues and eigenvectors. Furthermore, we propose a novel jackknife-type estimator of the asymptotic variance of the integrated volatility functional estimator. This new variance estimator shows much better finite sample performances compared to other existing ones. This paper also proposes several statistical tests for some commonly tested hypotheses in the literature. Simulation results show that one will get misleading results if one uses the analytical results of the covariance case when applying PCA on the correlation matrix.

The analysis of recurrent events in the presence of terminal events requires special attention. Several approaches have been suggested for such analyses either using intensity models or marginal models. When analysing treatment effects on recurrent events in controlled trials, special attention should be paid to competing deaths and their impact on interpretation. This paper proposes a method that formulates a marginal model for recurrent events and terminal events simultaneously. Estimation is based on pseudo-observations for both the expected number of events and survival probabilities. Various relevant hypothesis tests in the framework are explored. Theoretical derivations and simulation studies are conducted to investigate the behaviour of the method. The method is applied to two real data examples. The bivariate marginal pseudo-observation model carries the strength of a two-dimensional modelling procedure and performs well in comparison with available models. Finally, an extension to a three-dimensional model, which decomposes the terminal event per death cause, is proposed and exemplified.

Bias correction in predictive regressions is known to reduce the empirical size problems of OLS-based predictability tests with persistent predictors. This paper shows that bias correction is also achieved in the context of the extended instrumental variable (IVX) predictability testing framework introduced by Kostakis et al. (2015). To be specific, new IVX-based statistics subject to a bias correction analogous to that proposed by Amihud and Hurvich (2004) are introduced. Four important contributions are provided: first, we characterize the effects that bias-reduction adjustments have on the asymptotic distributions of the IVX test statistics in a general context allowing for short-run dynamics and heterogeneity; second, we discuss the validity of the procedure when predictors are stationary as well as near-integrated; third, we conduct an exhaustive Monte Carlo analysis to investigate the small in- and out-of-sample properties of the test procedures and their sensitivity to distinctive features that characterize predictive regressions in practice, such as strong persistence, endogeneity, and non-Gaussian innovations; and fourth, we provide an analysis of real estate return and rent growth predictability in 19 OECD countries.

Maurer's universal statistical test can widely detect non-randomness of given sequences. Coron proposed an improved test, and further Yamamoto and Liu proposed a new test based on Coron's test. These tests use normal distributions as their reference distributions, but the soundness has not been theoretically discussed so far. Additionally, Yamamoto and Liu's test uses an experimental value as the variance of its reference distribution. In this paper, we theoretically derive the variance of the reference distribution of Yamamoto and Liu's test and prove that the true reference distribution of Coron's test converges to a normal distribution in some sense. We can apply the proof to the other tests with small changes.

The problem of constructing the most powerful test for random number generators (RNGs) is considered, where the generators are modelled by stationary ergodic processes. At present, RNGs are widely used in data protection, modelling and simulation systems, computer games, and in many other areas where the generated random numbers should look like binary numbers of a Bernoulli equiprobable sequence. Another problem considered is that of constructing effective statistical tests for random number generators (RNG). Currently, effectiveness of statistical tests for RNGs is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p -value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p -value for any (unknown) stationary ergodic source. This model appears to be acceptable for binary sequences generated by physical devices that are used in cryptographic data protection systems.

Generative adversarial networks (GANs) have emerged as a powerful generative model in computer vision. Given their impressive abilities in generating highly realistic images, they are also being used in novel ways in applications in the life sciences. This raises an interesting question when GANs are used in scientific or biomedical studies. Consider the setting where we are restricted to only using the samples from a trained GAN for downstream group difference analysis (and do not have direct access to the real data). Will we obtain similar conclusions? In this work, we explore if “generated” data, i.e., sampled from such GANs can be used for performing statistical group difference tests in cases versus controls studies, common across many scientific disciplines. We provide a detailed analysis describing regimes where this may be feasible. We complement the technical results with an empirical study focused on the analysis of cortical thickness on brain mesh surfaces in an Alzheimer’s disease dataset. To exploit the geometric nature of the data, we use simple ideas from spectral graph theory to show how adjustments to existing GANs can yield improvements. We also give a generalization error bound by extending recent results on Neural Network Distance. To our knowledge, our work offers the first analysis assessing whether the Null distribution in “healthy versus diseased subjects” type statistical testing using data generated from the GANs coincides with the one obtained from the same analysis with real data. The code is available at https://github.com/yyxiongzju/GLapGAN.

Conformal prediction is an attractive framework for prediction that is distribution free. In this article, we study in details its homeostasis property under a general regression setup and also introduce the concepts of upper and lower predictive distributions and predictive curve to establish connections to left-, right- and two-tailed hypothesis testing problems as well as the developments in confidence distributions. The homeostasis property is very attractive, since it states that under some conditions the prediction results remain valid even if the model used for learning is completely wrong. We show explicitly why the property holds in a model-based setup and also explore the boundary when the property breaks down. Beside the typical assumption used in conformal prediction that the response and covariate pairs ( y , x ) of all subjects are iid distributed, we also study the classical regression setting in which the design is fixed with given (non-random) covariates x. The trade-offs among learning model accuracy, prediction valid and prediction efficiency are discussed, leading to an emphasis of more efforts on developing better learning models.

In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that contains two developments. First, we propose a faster numerical procedure in computing the moments of the quadratic forms. Second, we establish a general moment-matching framework for distribution approximation, which covers existing approximation methods for the distributions of the quadratic forms of Gaussian variables. Under this framework, a novel moment-ratio method (MR) is proposed to match the ratio of skewness and kurtosis based on the gamma distribution. Our extensive simulations show that 1) MR is almost as accurate as the exact distribution calculation and is much more efficient; 2) comparing with existing approximation methods, MR significantly improves the accuracy of approximating far right tail probabilities. The proposed method has wide applications. For example, it is a better choice than existing methods for facilitating hypothesis testing in big data analysis, where efficient and accurate calculation of very small $p$-values is desired. An R package Qapprox that implements related methods is available on CRAN.

With few exceptions, simulation output analysis has focused on static characterizations, to determine a property of the steady-state distribution of a performance metric such as a mean, a quantile, or the distribution itself. Analyses often seek to overcome difficulties induced by autocorrelation of the output stream. But sample paths generated by stochastic simulation exhibit dynamic behaviour that is characteristic of system structure and associated distributions. In this paper, we explore these dynamic characteristics, as captured by the Fourier transform of a dynamic steady-state simulation trajectory. We find that Fourier coefficient magnitudes can have greater discriminatory power than the usual test statistics when two systems have different utilisations and/or dynamic behaviour, and with simpler analysis resulting from the statistical independence of coefficient estimates at different frequencies.

This paper suggests a new hybrid algorithm by integrating two population-based algorithms: Whale Optimization Algorithm (WOA) and Flower Pollination Algorithm (FPA), to solve complex nonlinear systems and unconstrained optimization problems. WOFPA denotes the suggested algorithm, a hybrid Whale Optimization Algorithm and Flower Pollination Algorithm. Nonlinear systems can be cast into unconstrained optimization problems, called merit functions, where the optimal solutions for the merit functions are equivalent to the solutions of nonlinear systems. WOFPA aims to decrease the execution time and the complexity of WOA and FPA. WOFPA has the advantages of WOA and FPA; WOFPA is a high-quality algorithm to solve both problems, nonlinear systems and unconstrained optimization problems. For example, FPA may have a premature convergence in the local optima, and WOFPA subdues the disadvantage of FPA. Numerical experiments of 14 benchmarks nonlinear systems and 30 CEC 2014 benchmarks unconstrained optimization functions with various dimensions are employed to test the performance of WOFPA. To have a further investigation for the performance of WOFPA, WOFPA is compared with WOA, FPA, and other existing algorithms from the literature. Two non-parametric statistical tests, Wilcoxon statistical test and the Friedman test, are conducted for this study to check the performance of the proposed algorithms and other compared algorithms and the significance of our results. The experiment results demonstrate that WOFPA performs better than other algorithms in the literature by getting the optimum solutions for most nonlinear systems and optimization problems and proves its efficiency compared with other existing algorithms.

Variability assessment of qualitative data has an important role in diverse areas such as sociology, quality engineering, healthcare, decision making, genetics, metrology in chemistry and many others. To test the homogeneity hypothesis, we use two main categorical factors. Using a cross-balanced design, we provide a decomposition theorem of the sample total-variation into ‘intra’ (within) component and ‘inter’ (between) component for any scale. Building on this, we provide a way for decomposing the ‘inter’ component itself into variation components contributed by the two factors and their interaction (when we consider more than one replicated test in the cross-design). Moreover, focusing on an ordinal scale, we offer segregation power indices for testing the significate effects of the two factors and their interaction. A two-way ORDANOVA calculator is provided to display the empirical distributions of the segregation power indices and to find critical points of the test statistics distributions at the given confidence level. Some examples are given to demonstrate the proposed method.

In recent years, integer-valued time series attract the attention of researchers and find their applications in data analysis. Among various models, the integer-valued autoregressive (INAR) ones are of great popularity and are widely applied in practice. This paper develops some portmanteau test statistics to check the adequacy of the fitted model in a wide group of INAR processes, called generalized INAR. For this purpose, the asymptotic distributions of the test statistics are obtained and, using Monte Carlo simulation studies, their finite sample properties are derived. Besides, the results are applied in analyzing a real data example

The likelihood ratio test is one of the commonly used procedures for hypothesis testing. Several results on likelihood ratio test have been discussed for testing the scale parameter of an exponential distribution under complete and censored data; however, all of them are based on approximations of the involved null distributions. In this paper, we first derive the exact distribution of the likelihood ratio statistic for testing the scale parameter of an exponential distribution based on a time-constrained life-testing experiment. We also obtain the asymptotic distribution, which is useful in the case of a large sample size. We then discuss the derivation of its power function. Next, we consider the likelihood ratio test of $$\theta _2=\gamma _0\theta _1$$ when data are obtained from two exponential distributions based on a time-constrained life-testing experiment. Here again, we derive both exact and asymptotic distributions of the likelihood ratio statistic and then use them to determine the reject region as well as the power function. Monte Carlo simulations are then carried out to evaluate the performance of the inferential methods developed here. Finally, some examples are used to illustrate all the inferential results.

We consider a model whereby a given response variable Y following a transformation $${{\mathcal {Y}}}:=\mathcal {T}(Y)$$ , satisfies some classical regression equation. In this transformation model the form of the transformation is specified analytically but incorporates an unknown transformation parameter. We develop testing procedures for the null hypothesis of homoskedasticity for versions of this model where the regression function is considered either known or unknown. The test statistics are formulated on the basis of Fourier-type conditional contrasts of a variance computed under the null hypothesis against the same quantity computed under alternatives. The limit null distribution of the test statistic is studied, as well as the behaviour of the test criterion under alternatives. Since the limit null distribution is complicated, a bootstrap version is suggested in order to actually carry out the test procedures. Monte Carlo results are included that illustrate the finite-sample properties of the new method. The applicability of the new tests on real data is also illustrated.

We study statistical inference for stochastic partial differential equations (SPDEs). Though inference linear SPDEs have been studied well (with lot of problems still remain to be investigated) in the last two decades, inference for nonlinear SPDEs is in its infancy. The inference methods use both inference for finite-dimensional diffusions and inference for classical i.i.d. sequences. Solving 2D Navier-Stokes equation is one of the challenging problem of the last century. However, with additive white noise, the equation has a strong solution. We estimate the viscosity coefficient of the 2D stochastic Navier-Stokes (SNS) equation by minimum contrast method. We show $n$ consistency in contrast to $\sqrt n$ consistency in the classical i.i.d. case where $n$ is the number of observations. We consider both continuous and discrete observations in time. We also obtain the Berry-Esseen bounds. Then we estimate and control the Type I and Type II error of a simple hypothesis testing problem of the viscosity coefficient of the SNS equation. We study a class of rejection regions and provide thresholds that guarantee that the statistical errors are smaller than the given upper bound. The tests are of likelihood ratio type. The proofs are based on the large deviation bounds. Finally we give Monte Carlo test procedure for simulated data.

Background Patterns of multi-locus differentiation (i.e., genomic clines) often extend broadly across hybrid zones and their quantification can help diagnose how species boundaries are shaped by adaptive processes, both intrinsic and extrinsic. In this sense, the transitioning of loci across admixed individuals can be contrasted as a function of the genome-wide trend, in turn allowing an expansion of clinal theory across a much wider array of biodiversity. However, computational tools that serve to interpret and consequently visualize ‘genomic clines’ are limited, and users must often write custom, relatively complex code to do so. Results Here, we introduce the ClineHelpR R-package for visualizing genomic clines and detecting outlier loci using output generated by two popular software packages, bgc and Introgress. ClineHelpR bundles both input generation (i.e., filtering datasets and creating specialized file formats) and output processing (e.g., MCMC thinning and burn-in) with functions that directly facilitate interpretation and hypothesis testing. Tools are also provided for post-hoc analyses that interface with external packages such as ENMeval and RIdeogram. Conclusions Our package increases the reproducibility and accessibility of genomic cline methods, thus allowing an expanded user base and promoting these methods as mechanisms to address diverse evolutionary questions in both model and non-model organisms. Furthermore, the ClineHelpR extended functionality can evaluate genomic clines in the context of spatial and environmental features, allowing users to explore underlying processes potentially contributing to the observed patterns and helping facilitate effective conservation management strategies.

This paper discusses a non-parametric resampling technique in the context of multidimensional or multiparameter hypothesis testing of assumptions of the Rasch model. It is based on conditional distributions and it is suggested in small sample size scenarios as an alternative to the application of asymptotic or large sample theory. The exact sampling distribution of various well-known chi-square test statistics like Wald, likelihood ratio, score, and gradient tests as well as others can be arbitrarily well approximated in this way. A procedure to compute the power function of the tests is also presented. A number of examples of scenarios are discussed in which the power function of the test does not converge to 1 with an increasing deviation of the true values of the parameters of interest from the values specified in the hypothesis to be tested. Finally, an attempt to modify the critical region of the tests is made aiming at improving the power and an R package is provided.

F 2 -linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer from linear artifacts that show as failures in linearity-related statistical tests such as the binary-rank and the linear-complexity test. In this article, we give two new contributions. First, we introduce two new F 2 -linear transformations that have been handcrafted to have good statistical properties and at the same time to be programmable very efficiently on superscalar processors, or even directly in hardware. Then, we describe some scramblers , that is, nonlinear functions applied to the state array that reduce or delete the linear artifacts, and propose combinations of linear transformations and scramblers that give extremely fast pseudorandom number generators of high quality. A novelty in our approach is that we use ideas from the theory of filtered linear-feedback shift registers to prove some properties of our scramblers, rather than relying purely on heuristics. In the end, we provide simple, extremely fast generators that use a few hundred bits of memory, have provable properties, and pass strong statistical tests.

Asymptotic properties of robust regression estimators are well known. However, it is not always clear what is the best strategy for confidence intervals and hypothesis testing when the sample size is not very large, since the distribution of residuals coming from robust estimates has unknown properties for small samples. In the present work we propose an analysis of various strategies for estimating the variance-covariance matrix of the S estimators at the variation of n and p, considering different �� functions. An adaptive correction strategy is proposed. In addition to the simulation study, an example on a benchmark dataset is shown.

We propose test statistics for testing for the equivalence of the mean functions with respect to time for two sets of time series and that for several sets of time series. We also propose multiple ...

Summary The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross-sectional dependence is considered. Under the assumption that the cross-sectional dependence is captured by an unknown number of common factors, a new CUSUM-type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross sectional time series of length T, the asymptotic results hold under the mild assumption that $\min \lbrace N,T\rbrace \rightarrow \infty$, with an otherwise arbitrary relationship between N and T, allowing the results to apply to most panel data examples. Bootstrap procedures are proposed to approximate the sampling distribution of the test statistics. A Monte Carlo simulation study showed that our test outperforms several other existing tests in finite samples in a number of cases, particularly when N is much larger than T. The practical application of the proposed results are demonstrated with real data applications to detecting and estimating change points in the high dimensional FRED-MD macroeconomic data set.

Using the criterion of the minimum average risk, the statistically optimal algorithm for identifying objects by the same type of parameters is synthesized for the structural and system monitoring of the situation. In order to reduce computational costs, its quasi-optimal modification is performed, based on the exclusion of significantly different parameter values from the compared arrays. An identification simulation model is developed in the Qt Creator software environment in the object-oriented C++ programming language. Based on the statistical tests of the model, the probabilities of correctly identifying objects and false alarms are investigated according to estimates of the maximum likelihood of angular coordinates. The dependences of the indicators of identification efficiency on the root mean square errors (RMSEs) of the parameter estimates, the number of objects, and their density in the monitoring area are analyzed.

We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) t -statistic is considered, and we determine its rejection region using a common rejection limit. When there are unknown correlations among test statistics, the multiplicity adjusted p -values are dependent on the unknown correlations. They are usually replaced with their estimates that are always consistent under any hypothesis. In this paper, we propose the use of estimates, which are not necessarily consistent and are referred to as spurious correlations, in order to improve statistical power. Through simulation studies, we verify that the proposed method asymptotically controls the family-wise error rate and clearly provides higher statistical power than existing methods. In addition, the proposed and existing methods are applied to a real multiple testing problem that compares quantitative traits among groups of mice and the results are compared.

The psychometric process used to establish a relationship between the scores of two (or more) instruments is generically referred to as linking. When two instruments with the same content and statistical test specifications are linked, these instruments are said to be equated. Linking and equating procedures have long been used for practical benefit in educational testing. In recent years, health outcome researchers have increasingly applied linking techniques to patient-reported outcome (PRO) data. However, these applications have some noteworthy purposes and associated methodological questions. Purposes for linking health outcomes include the harmonization of data across studies or settings (enabling increased power in hypothesis testing), the aggregation of summed score data by means of score crosswalk tables, and score conversion in clinical settings where new instruments are introduced, but an interpretable connection to historical data is needed. When two PRO instruments are linked, assumptions for equating are typically not met and the extent to which those assumptions are violated becomes a decision point around how (and whether) to proceed with linking. We demonstrate multiple linking procedures—equipercentile, unidimensional IRT calibration, and calibrated projection—with the Patient-Reported Outcomes Measurement Information System Depression bank and the Patient Health Questionnaire-9. We validate this link across two samples and simulate different instrument correlation levels to provide guidance around which linking method is preferred. Finally, we discuss some remaining issues and directions for psychometric research in linking PRO instruments.

We develop new tests for the linear relationship between temperature and forcing, which is one of the most studied implications from a simple energy balance model. We consider a bivariate system of temperature and forcing where the time path of well-mixed-greenhouse-gases forcing is included as a potential common trend function in addition to a stochastic trend and a broken linear trend. Our test statistics are first devised as the likelihood ratio and then are modified to remove nuisance parameters in the asymptotic null distribution. The asymptotic null distribution and the required modification differ as to the existence of a stochastic trend. Thus, the test statistics are modified in two different ways and then are combined using the super-efficient estimator of the sum of autoregressive coefficients. The asymptotic critical values from the two cases remain close and we use the bigger one to control size for both cases. The proposed tests are applied to four temperature series and a forcing series. The null hypothesis of the linear relationship is not rejected with conventional sizes.

This paper is concerned with the intermittent fault (IF) detection problem for a class of linear discrete-time stochastic systems over sensor networks with constant time delay. By utilizing the lifting method, the distributed decoupled observers are proposed based on the output information of neighbor nodes and the node itself. In order to detect the appearing time and disappearing time of the IF, the truncated residuals are designed by introducing a sliding-time window. Furthermore, the IF detection and location thresholds are determined based on the hypothesis testing technique and the detectability of the IF is analyzed in the framework of stochastic analysis. Finally, a simulation example is presented to illustrate the effectiveness of the derived results.

The two-parameter Birnbaum–Saunders distribution was derived to describe the failure time from a process of fatigue crack growth. The scale parameter is also the median of the distribution. The inf...

We propose a kernel density based estimation for multiplicative linear regression models. The method proposed in this article makes use of kernel smoothing nonparametric techniques to estimate the unknown density function of model error. For the hypothesis testing of parametric components, restricted estimators under the null hypothesis and test statistics are proposed. The asymptotic properties for the estimators and test statistics are established. We illustrate our proposals through simulations and an analysis of the QSAR fish bioconcentration factor data set. Our analysis provides strong evidence that the proposed kernel density based estimator is superior than the least squares estimator and least product relative error estimator in the literature, particularly for multimodal or asymmetric or heavy-tailed distributions of the model error.

This paper considers an extension of the linear non-Gaussian acyclic model (LiNGAM) that determines the causal order among variables from a dataset when the variables are expressed by a set of linear equations, including noise. In particular, we assume that the variables are binary. The existing LiNGAM assumes that no confounding is present, which is restrictive in practice. Based on the concept of independent component analysis (ICA), this paper proposes an extended framework in which the mutual information among the noises is minimized. Another significant contribution is to reduce the realization to the shortest path problem, in which the distance between each pair of nodes expresses an associated mutual information value, and the path with the minimum sum (KL divergence) is sought. Although p! mutual information values should be compared, this paper dramatically reduces the computation when no confounding is present. The proposed algorithm finds the globally optimal solution, while the existing approaches locally greedily seek the order based on hypothesis testing. We use the best estimator in the sense of Bayes/MDL that correctly detects independence for mutual information estimation. Experiments using artificial and actual data show that the proposed version of LiNGAM achieves significantly better performance, particularly when confounding is present.

We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $$\theta ^*$$ which may change over time. We propose procedures which are based on the Poisson quasi-maximum likelihood estimator of the parameter, and where the updated estimator is computed without the historical observations in the sequential framework. For both the retrospective and the sequential detection, the test statistics converge to some distributions obtained from the standard Brownian motion under the null hypothesis of no change and diverge to infinity under the alternative; that is, these procedures are consistent. Some results of simulations as well as real data application are provided.

We use distance covariance to introduce novel consistent tests of heteroscedasticity for nonlinear regression models in multidimensional spaces. The proposed tests require no user-defined regularization, which are simple to implement based on only pairwise distances between points in the sample and are applicable even if we have non-normal errors and many covariates in the regression model. We establish the asymptotic distributions of the proposed test statistics under the null and alternative hypotheses and a sequence of local alternatives converging to the null at the fastest possible parametric rate. In particular, we focus on whether and how the estimation of the finite-dimensional unknown parameter vector in regression functions will affect the distribution theory. It turns out that the asymptotic null distributions of the suggested test statistics depend on the data generating process, and then a bootstrap scheme and its validity are considered. Simulation studies demonstrate the versatility of our tests in comparison with the score test, the Cramer-von Mises test, the Kolmogorov-Smirnov test and the Zheng-type test. We also use the ultrasonic reference block data set from National Institute for Standards and Technology of USA to illustrate the practicability of our proposals.

The conditional approach of Hill's estimator depends on a threshold choice. This may give different results in a statistical test when different thresholds are used. Motivated by the uniformly most...

Kejriwal and Perron (2010, KP) provided a comprehensive treatment for the problem of testing multiple structural changes in cointegrated regression models. A variety of models were considered depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held A–xed (partial structural change). In this note, we A–rst show that the limit distributions of the test statistics in the latter case are not invariant to changes in the coe¢ cients not being tested; in fact, they diverge as the sample size increases. To address this issue, we propose a simple two step procedure to test for partial parameter stability. The A–rst entails the application of a joint test of stability for all coe¢ cients as in KP. Upon a rejection, the second conducts a stability test on the subset of coe¢ cients of interest while allowing the other coe¢ cients to change at the estimated breakpoints. Its limit distribution is standard chi-square. The relevant asymptotic theory is provided along with simulations that illustrates the usefulness of the procedure in finite samples.

Over the years, numerous fuzzy time-series forecasting (FTSF) models have been developed to handle the uncertainty and non-determinism in the time-series (TS) data. To handle the non-determinism and indeterminacy, researchers have considered either intuitionistic fuzzy set or hesitant fuzzy set theory. However, in both the fuzzy set theories (FST), the degree of indeterminacy is a dependent value and always lies in the range [0, 1]. Hence, these two fuzzy set theories fail to model the indeterminacy value when the degree of non-membership fluctuates due to hesitancy. Motivated from this, we have considered neutrosophic entropy-based fuzzy time-series forecasting (NEBFTSF) model where the neutrosophic entropy of each observation in the TS is used to capture the indeterminacy. Apart from this, the triangular membership value for each observation is used to illustrate the non-probabilistic uncertainty in the TS. The present research mainly focuses on three concepts such as 1) an adaptive method is used to partition the universe of discourse (UOD) into unequal length of intervals (LOIs), 2) for the first time the fuzzy logical relationships (FLRs) are established by considering the ratio trend variation (RTV) data with mean of aggregated entropy value of each crisp observation, and 3) to obtain the forecasted values both de-trending and de-normalization are employed. To assess the forecasting performance of the proposed model, 11 TS datasets with ten distinct profound forecasting models are considered. The Friedman and Nemenyi hypothesis test and Wilcoxon signed rank test conform the forecasting efficiency and reliability of the NEBFTSF model.

In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a discrete point mass at zero and a continuous skewed positive component, and hence such distribution is semicontinuous in the nature. To utilize the information from both populations, we model the positive components of the two mixture distributions via a semiparametric density ratio model. Under this model setup, we construct the maximum empirical likelihood estimators of the linear functionals and their functions, and establish the asymptotic normality of the proposed estimators. We show the proposed estimators of the linear functionals are more efficient than the fully nonparametric ones. The developed asymptotic results enable us to construct confidence regions and perform hypothesis tests for the linear functionals and their functions. We further apply these results to several important summary quantities such as the moments, the mean ratio, the coefficient of variation, and the generalized entropy class of inequality measures. Simulation studies demonstrate the advantages of our proposed semiparametric method over some existing methods. Two real data examples are provided for illustration., Comment: 32 pages

In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous-time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and countable state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates.

High-dimensional data are frequently encountered with the development of modern data collection techniques. Testing the equality of the mean vectors of two high-dimensional samples with possibly different covariance matrices is usually referred to as a high-dimensional two-sample Behrens–Fisher (BF) problem. In the high-dimensional setting, the classical BF solutions are expected to perform poorly or become inapplicable due to the singularity of the sample covariance matrices. Several approaches have been proposed in the literature to address this challenging issue but they all require strong regularity conditions on the underlying covariance matrices to guarantee that their test statistics are asymptotically normally distributed. To overcome this difficulty, an L 2 -norm-based test is proposed and studied in this article. It is shown that under some regularity conditions and the null hypothesis, the test statistic and a chi-square-type mixture have the same normal or non-normal limiting distribution. It is then natural to approximate the null distribution of the proposed test using that of the chi-square-type mixture, which is actually obtained from the proposed test statistic when the two high-dimensional samples are normally distributed. The resulting test is then referred to as a normal reference test. The distribution of the chi-square-type mixture can then be well approximated by the Welch–Satterthwaite χ 2 -approximation with the approximation parameters consistently estimated from the data. The asymptotic power of the proposed test is established. Good performance of the proposed test against several existing competitors is demonstrated via several simulation studies and illustrated by a real data example.

In this work, we approximated a set of unknown physical parameters for a semi-empirical mathematical model of a PEMFC. We used an Estimation of Distribution Algorithm (EDA) known as U M D A G to find the tuple that best reproduces the experimental polarization curve. We tackled non-derivable objective functions to perform robust parameter estimation. We compared the sum of the squared error with published results, and the sum and the median of the absolute error values were used to diminish or remove the effect of possible noise or outliers. Since the U M D A G requires a single user-given parameter (the population size) and presents a natural reduction of the variance, it was possible to introduce a variance-based stopping criterion. The obtained results were compared with the most up-to-date evolutionary algorithms, demonstrating that this proposal is competitive. We used four previously reported experimental datasets to get the parameters or validate them. Two of them were used to test the method and to compare it with reported results of recent bio-inspired metaheuristics. Then, we used the identified parameters to simulate the cases of the remaining data sets validating the correct estimation. Finally, we introduced a posterior statistical analysis (hypothesis test), which provided further information about dependencies and the impact of each parameter on the cell performance.

Temporal changes in medical images are often evaluated along a parametrized function that represents a structure of interest (e.g. white matter tracts). By attributing samples along these functions with distributions of image properties in the local neighborhood, we create distribution-valued signatures for these functions. We propose a novel, comprehensive framework which models their temporal evolution trajectories. This is achieved under the unifying scheme of Wasserstein distance metric. The regression problem is formulated as a constrained optimization problem and solved using an alternating projection algorithm. The solution simultaneously preserves the functional characteristics of the curve, models the temporal change in distribution profiles and forces the estimated distributions to be valid. Hypothesis testing is applied in two ways using Wasserstein based test statistics. Validation is presented on synthetic data. Estimation of a population trajectory is shown using diffusion properties along DTI tracts from a healthy population of infants. Detection of delayed growth is shown using a case study.

For vector Ito semimartingale dynamics, we derive the asymptotic distributions of likelihood-ratio-type test statistics for the purpose of identifying the eigenvalue structure of both integrated and spot covariance matrices estimated using high-frequency data. Unlike the existing approaches where the cross-section dimension grows to infinity, our tests do not necessarily require large cross-section and thus allow for a wide range of applications. The tests, however, are based on non-standard asymptotic distributions with many nuisance parameters. Another contribution of this paper consists in proposing a bootstrap method to approximate these asymptotic distributions. While standard bootstrap methods focus on sampling point-wise returns, the proposed method replicates features of the asymptotic approximation of the statistics of interest that guarantee its validity. A Monte Carlo simulation study shows that the bootstrap-based test controls size and has power for even moderate size samples.

This study aims to determine how the influence of religious knowledge and religiosity on pluralism of students Kajen. This research is quantitative with three variables, they are religious knowledge and religiosity as independent variables, and pluralism as dependent variable. Data analyzing of this research used the correlation of product moment for the partial test, and linear regression test for the simultaneous test. The results of data analysis to the 136 samples showed that there is a positive and significant correlation between religious knowledge and pluralism, it shown by the value of sig is smaller than the value of alpha. Furthermore, the second hypothesis test showed the same results that there is a positive and significant relationship between religiosity and pluralism, the value of sig 0,0003,00, it means that religious knowledge and religiosity influence together on pluralism. Equation of regression’s line Y=0,511X_1+0,274X_2+44,728, showed that the value of coefficient X1 and X2 is positive, means both of them influence on pluralism positively (Y).

For high-dimensional nonparametric Behrens-Fisher problem in which the data dimension is larger than the sample size, the authors propose two test statistics in which one is U-statistic Rank-based Test (URT) and another is Cauchy Combination Test (CCT). CCT is analogous to the maximum-type test, while URT takes into account the sum of squares of differences of ranked samples in different dimensions, which is free of shapes of distributions and robust to outliers. The asymptotic distribution of URT is derived and the closed form for calculating the statistical significance of CCT is given. Extensive simulation studies are conducted to evaluate the finite sample power performance of the statistics by comparing with the existing method. The simulation results show that our URT is robust and powerful method, meanwhile, its practicability and effectiveness can be illustrated by an application to the gene expression data.