Search

We define a random zonotope in R d , by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine, under a mild assumption on the distribution, the expectations of the intrinsic volumes, more generally, the expectations of suitable valuations. We also prove a central limit theorem for a valuation evaluated at these random zonotopes. [ABSTRACT FROM AUTHOR]

The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, we develop a second-order U-statistic using a pseudo-estimate for the unknown non-parametric component. Under some regularity conditions, the asymptotic normality of the proposed test statistic is established using the martingale central limit theorem. The proposed test is evaluated for finite sample properties through simulation studies and its application to real data. [ABSTRACT FROM AUTHOR]

With our increased ability to capture large data, causal inference has received renewed attention and is playing an ever-important role in biomedicine and economics. However, one major methodological hurdle is that existing methods rely on many unverifiable model assumptions. Thus robust modeling is a critically important approach complementary to sensitivity analysis, where it compares results under various model assumptions. The more robust a method is with respect to model assumptions, the more worthy it is. The doubly robust estimator (DRE) is a significant advance in this direction. However, in practice, many outcome measures are functionals of multiple distributions, and so are the associated estimands, which can only be estimated via U-statistics. Thus most existing DREs do not apply. This article proposes a broad class of highly robust U-statistic estimators (HREs), which use semiparametric specifications for both the propensity score and outcome models in constructing the U-statistic. Thus, the HRE is more robust than the existing DREs. We derive comprehensive asymptotic properties of the proposed estimators and perform extensive simulation studies to evaluate their finite sample performance and compare them with the corresponding parametric U-statistics and the naive estimators, which show significant advantages. Then we apply the method to analyze a clinical trial from the AIDS Clinical Trials Group. [ABSTRACT FROM AUTHOR]

We derive limiting distributions of symmetrized estimators of scatter. Instead of considering all n (n - 1) / 2 pairs of the n observations, we only use nd suitably chosen pairs, where d ≥ 1 is substantially smaller than n. It turns out that the resulting estimators are asymptotically equivalent to the original one whenever d = d (n) → ∞ at arbitrarily slow speed. We also investigate the asymptotic properties for arbitrary fixed d. These considerations and numerical examples indicate that for practical purposes, moderate fixed values of d between 10 and 20 yield already estimators which are computationally feasible and rather close to the original ones. [ABSTRACT FROM AUTHOR]

It is shown that higher-order influence functions for M-estimators are mathematically equivalent to higher-order stochastic approximations to these estimators. The stochastic expansions are also shown to have corresponding higher-order U-statistic representations, providing an alternative approach for deriving and analyzing the approximate properties of M-estimators. [ABSTRACT FROM AUTHOR]

We develop new goodness of fit tests for Rayleigh distribution based on fixed point characterization. We use U-Statistic theory to derive the test statistics. First we develop a test for complete data and then discuss, how the right censored observations can be incorporated in the testing procedure. The asymptotic properties of the test statistic in both uncensored and censored cases are studied in detail. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed tests. We illustrate the procedures using real data sets. We also provide, a goodness of fit test for the standard Rayleigh distribution based on jackknife empirical likelihood. [ABSTRACT FROM AUTHOR]

The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, we develop a second-order U-statistic using a pseudo-estimate for the unknown non-parametric component. Under some regularity conditions, the asymptotic normality of the proposed test statistic is established using the martingale central limit theorem. The proposed test is evaluated for finite sample properties through simulation studies and its application to real data.

Poisson processes in the space of k -dimensional totally geodesic subspaces (k -flats) in a d -dimensional standard space of constant curvature κ ∈ { − 1 , 0 , 1 } are studied, whose distributions are invariant under the isometries of the space. We consider the intersection processes of order m together with their (d − m (d − k)) -dimensional Hausdorff measure within a geodesic ball of radius r. Asymptotic normality for fixed r is shown as the intensity of the underlying Poisson process tends to infinity for all m satisfying d − m (d − k) ≥ 0. For κ ∈ { − 1 , 0 } the problem is also approached in the set-up where the intensity is fixed and r tends to infinity. Again, if 2 k ≤ d + 1 a central limit theorem is shown for all possible values of m. However, while for κ = 0 asymptotic normality still holds if 2 k > d + 1 , we prove for κ = − 1 convergence to a non-Gaussian infinitely divisible limit distribution in the special case m = 1. The proof of asymptotic normality is based on the analysis of variances and general bounds available from the Malliavin–Stein method. We also show for general κ ∈ { − 1 , 0 , 1 } that, roughly speaking, the variances within a general observation window W are maximal if and only if W is a geodesic ball having the same volume as W. Along the way we derive a new integral-geometric formula of Blaschke–Petkantschin type in a standard space of constant curvature. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic distribution of some U-statistics whose entries are functions of empirical moments computed from non-overlapping consecutive blocks of an underlying weakly dependent process. The length of these blocks converges to infinity, and thus we consider U-statistics of triangular arrays. We establish asymptotic normality of such U-statistics. The results can be used to construct tests for changes of higher order moments. [ABSTRACT FROM AUTHOR]

This paper introduces two local conditional dependence matrices based on Spearman's ρ and Kendall's τ given the condition that the underlying random variables belong to the intervals determined by their quantiles. The robustness is studied by means of the influence functions of conditional Spearman's ρ and Kendall's τ. Using the two matrices, we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency, null and alternative asymptotic distributions. Simulation studies illustrate a superior power performance of the proposed Kendall-based test. Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics. [ABSTRACT FROM AUTHOR]

Due to the complexity of the data being generated day in and day out in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability called the classes of life and determinant probability distributions has been presented. This article introduces novel statistical probability models for the reliability class of life test under different reliability processes in the age range t ∘ . Several probabilistic properties and features were derived and rigorously screened to test the new reliability class. According to the U-statistic, a novel hypothesis test was created to evaluate the exponentiality property. The comparative efficiency of the test according to Pitman's asymptotic efficiency was examined and compared with other reliability classes. To prove the superiority of the new reliability class, some probability models were utilized, including the Weibull, Makeham, gamma, and linear failure rate models. Moreover, critical point simulations of the null Monte Carlo distribution and some applications of the censored and uncensored data were implemented to validate the class test listed by the reliability analysis. [ABSTRACT FROM AUTHOR]

This article proposes a consistent nonparametric test for common trend specifications in panel data models with fixed effects. The test is general enough to allow for heteroscedasticity, cross-sectional and serial dependence in the error components, has an asymptotically normal distribution under the null hypothesis of correct trend specification, and is consistent against various alternatives that deviate from the null. In addition, the test has an asymptotic unit power against two classes of local alternatives approaching the null at different rates. We also propose a wild bootstrap procedure to better approximate the finite sample null distribution of the test statistic. Simulation results show that the proposed test implemented with bootstrap p-values performs reasonably well in finite samples. Finally, an empirical application to the analysis of the U.S. per capita personal income trend highlights the usefulness of our test in real datasets. [ABSTRACT FROM AUTHOR]

Technological advances have enabled us to collect a lot of complex data objects, where homogeneity structure among these objects is widely used in Statistics. However, the existing metrics of homogeneity are subject to some qualifications, such as assumptions about the moment and parameters. To overcome the limitation, this paper first introduces the characteristic distance, a novel metric that entirely characterizes the homogeneity of two distributions. The proposed distance possesses some desirable statistical properties: (i) It is a distribution-free or, more commonly, nonparametric test, thus is robust to the data; (ii) It is nonnegative and equal to zero if and only if the two distributions are homogeneous; (iii) The novel measure possesses a clear and intuitive probabilistic interpretation, moreover, its empirical version is easy to calculate and can be reduced to a sum of two V-statistics. Theoretically, the asymptotic distributions, including the mixture of χ 2 distributions under the null hypothesis and the asymptotic normality of the alternative hypothesis are thoroughly investigated. Simulation studies and a real data application suggest that the empirical characteristic distance has a preferable power in detecting the homogeneity of distributions. [ABSTRACT FROM AUTHOR]

Generalized linear models often have high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional subvector of the model's coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and are thus computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that, under certain regularity conditions, the Type-I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions. [ABSTRACT FROM AUTHOR]

Partially linear regression models are semiparametric models that contain both linear and nonlinear components. They are extensively used in many scientific fields for their flexibility and convenient interpretability. In such analyses, testing the significance of the regression coefficients in the linear component is typically a key focus. Under the high‐dimensional setting, i.e., "large p, small n," the conventional F‐test strategy does not apply because the coefficients need to be estimated through regularization techniques. In this article, we develop a new test using a U‐statistic of order two, relying on a pseudo‐estimate of the nonlinear component from the classical kernel method. Using the martingale central limit theorem, we prove the asymptotic normality of the proposed test statistic under some regularity conditions. We further demonstrate our proposed test's finite‐sample performance by simulation studies and by analyzing some breast cancer gene expression data. [ABSTRACT FROM AUTHOR]

The structure testing of a high-dimensional covariance matrix plays an important role in financial stock analyses, genetic series analyses, and many other fields. Testing that the covariance matrix is block-diagonal under the high-dimensional setting is the main focus of this paper. Several test procedures that rely on normality assumptions, two-diagonal block assumptions, or sub-block dimensionality assumptions have been proposed to tackle this problem. To relax these assumptions, we develop a test framework based on U-statistics, and the asymptotic distributions of the U-statistics are established under the null and local alternative hypotheses. Moreover, a test approach is developed for alternatives with different sparsity levels. Finally, both a simulation study and real data analysis demonstrate the performance of our proposed methods. [ABSTRACT FROM AUTHOR]

Copyright of Afrika Statistika is the property of Statistics & Probability African Society and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper addresses the problem of variance estimation of predictions obtained from a subsampling-based ensemble estimator, such as subbagging and sub-random forest. We first recognize that a subsampling-based ensemble can be written as an infinite-order U-statistic of degree k n , where k n is the subsample size that may depend on the learning sample size n. As a result, one can study the uncertainty of predictions obtained from a subsampling-based ensemble under a U-statistic framework, such as approximating its asymptotic variance. However, existing methods used to estimate the asymptotic variance relies on some regularity conditions. In addition, they tend to yield variance estimations with large bias in finite sample scenarios. Motivated by the work of Wang and Lindsay (2014), we propose to construct an unbiased variance estimator for a subsampling-based ensemble. It is efficient to realize with the help of a partition-resampling scheme. We show by simulation studies that the proposed variance estimator yields better performance in terms of mean, standard deviation, and mean squared error compared to both the infinitesimal jackknife and internal variance estimation methods under either a simple linear regression model or a multivariate adaptive regression splines model. Furthermore, we present how to construct an asymptotic confidence interval for the expected prediction at a given test instance using the proposed variance estimator, and compare its coverage probability to that of competing methods. In the end, we demonstrate the practical applications of the methodology using two real data examples. [ABSTRACT FROM AUTHOR]

We propose a consistent non‐parametric test for the correct specification of parametric trend functions in multi‐variate time series. The new test takes the form of the U‐statistic and is robust to serial and cross‐sectional dependence and time‐varying variances in error terms. The test statistic is shown to have a limiting standard normal distribution under the null and diverge to infinity under the alternative. Thus the test is consistent against any fixed alternative. The test is also shown to have non‐trivial asymptotic power against two classes of local alternatives approaching the null at different rates. A set of simulations is conducted to evaluate the finite‐sample performance of the test. [ABSTRACT FROM AUTHOR]

Disclosure is of fundamental interest to accounting research. When the sign/magnitude of disclosed news is unclear, the information in disclosure events is inferred using the ratio of return volatilities during event and non-event windows (Beaver 1968). We show that return noise due to microstructure frictions and mispricing affects this ratio, and that effect is comparable to or exceeds that of information content. We use the SEC's Tick Size Pilot program to confirm the causal effect of return noise on the ratio, and to evaluate alternative ways to control for it. The most promising approach is to use the difference between, rather than the ratio of, return volatilities during event and non-event windows. We illustrate its benefits by showing how it alters prior inferences regarding time-series and cross-sectional variation in information content as well as changes in the information content of earnings announcements around the 2004 amendments to Form 8-K filings. [ABSTRACT FROM AUTHOR]

The problem of assessing symmetry about an unspecified center of the one-dimensional marginal distribution of a strictly stationary random process is considered. A well-known U-statistic based on data triples is used to detect deviations from symmetry, allowing the underlying process to satisfy suitable mixing or near-epoch dependence conditions. We suggest using subsampling for inference on the target parameter, establish the asymptotic validity of the method in our setting, and discuss data-driven rules for selecting the size of subsamples. The small-sample properties of the proposed inferential procedures are examined by means of Monte Carlo simulations. Applications to time series of output growth and stock returns are also presented. [ABSTRACT FROM AUTHOR]

Originally proposed for the analysis of prioritized composite endpoints, the win ratio has now expanded into a broad class of methodology based on general pairwise comparisons. Complicated by the non‐i.i.d. structure of the test statistic, however, sample size estimation for the win ratio has lagged behind. In this article, we develop general and easy‐to‐use formulas to calculate sample size for win ratio analysis of different outcome types. In a nonparametric setting, the null variance of the test statistic is derived using U‐statistic theory in terms of a dispersion parameter called the standard rank deviation, an intrinsic characteristic of the null outcome distribution and the user‐defined rule of comparison. The effect size can be hypothesized either on the original scale of the population win ratio, or on the scale of a "usual" effect size suited to the outcome type. The latter approach allows one to measure the effect size by, for example, odds/continuation ratio for totally/partially ordered outcomes and hazard ratios for composite time‐to‐event outcomes. Simulation studies show that the derived formulas provide accurate estimates for the required sample size across different settings. As illustration, real data from two clinical studies of hepatic and cardiovascular diseases are used as pilot data to calculate sample sizes for future trials. [ABSTRACT FROM AUTHOR]

This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices. [ABSTRACT FROM AUTHOR]

We study the distribution of a general class of asymptotically linear statistics which are symmetric functions of N independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a remainder of order o (N - 1) . The Edgeworth expansion is based on Hoeffding's decomposition which provides a stochastic expansion into a linear part, a quadratic part as well as smaller higher order parts. The validity of this Edgeworth expansion is proved under Cramér's condition on the linear part, moment assumptions for all parts of the statistic and an optimal dimensionality requirement for the non linear part. [ABSTRACT FROM AUTHOR]

This paper develops methods to test for associations between two variables with clustered data using a U‐Statistic approach with a second‐order approximation to the variance of the parameter estimate for the test statistic. The tests that are presented are for clustered versions of: Pearsons χ2 test, the Spearman rank correlation and Kendall's τ for continuous data or ordinal data and for alternative measures of Kendall's τ that allow for ties in the data. Shih and Fay use the U‐Statistic approach but only consider a first‐order approximation. The first‐order approximation has inflated significance level in scenarios with small sample sizes. We derive the test statistics using the second‐order approximations aiming to improve the type I error rates. The method applies to data where clusters have the same number of measurements for each variable or where one of the variables may be measured once per cluster while the other variable may be measured multiple times. We evaluate the performance of the test statistics through simulation with small sample sizes. The methods are all available in the R package cluscor. [ABSTRACT FROM AUTHOR]

In this article, we consider the properties of the Pesaran CD test for cross-section correlation when applied to residuals obtained from panel data models with many estimated parameters. We show that the presence of period-specific parameters leads the CD test statistic to diverge as the time dimension of the sample grows. This result holds even if cross-section dependence is correctly accounted for and hence constitutes an example of the incidental parameters problem. The relevance of this problem is investigated for both the classical two-way fixed-effects estimator and the Common Correlated Effects estimator of Pesaran. We suggest a weighted CD test statistic which re-establishes standard normal inference under the null hypothesis. Given the widespread use of the CD test statistic to test for remaining cross-section correlation, our results have far reaching implications for empirical researchers. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Due to the complexity of the data being generated day in and day out in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability called the classes of life and determinant probability distributions has been presented. This article introduces novel statistical probability models for the reliability class of life test under different reliability processes in the age range t∘. Several probabilistic properties and features were derived and rigorously screened to test the new reliability class. According to the U-statistic, a novel hypothesis test was created to evaluate the exponentiality property. The comparative efficiency of the test according to Pitman’s asymptotic efficiency was examined and compared with other reliability classes. To prove the superiority of the new reliability class, some probability models were utilized, including the Weibull, Makeham, gamma, and linear failure rate models. Moreover, critical point simulations of the null Monte Carlo distribution and some applications of the censored and uncensored data were implemented to validate the class test listed by the reliability analysis.

There has been a recent upsurge of interest in testing for structural changes in heteroskedastic time series, as changes in the variance invalidate the asymptotic distribution of conventional structural change tests. Several tests have been proposed that are robust to general form of heteroskedastic errors. The most popular use a two‐steps approach: first estimate the residuals assuming no changes in the regression coefficients; second, use the residuals to approximate the heteroskedastic asymptotic distribution or take an entire sample average to construct a test for which the variance process is averaged out. An alternative approach was proposed by Perron et al. (Perron et al. (2020). Quantitative Economics11: 1019–1057) who provided a test for changes in the coefficients allowing for changes in the variance of the error term. We show that it transforms the variance profile into one that effectively has very little impact on the size of the test. With respect to the power properties, the two‐steps procedures can suffer from non‐monotonic power problems in dynamic models and in static models with a correction for serial correlation in the error. Most have power equals to size with zero‐mean regressors. Even when the two‐steps tests have power, it is generally lower than that of the latter test. [ABSTRACT FROM AUTHOR]

Testing the dependence between the response and the functional predictor in a functional linear model is of fundamental importance. In this paper, based on a U-statistic of order two, we develop a computationally more efficient test for lacking of dependence in functional linear regression model. By the martingale central limit theorem, we prove that the asymptotic normality of the proposed test statistic under some mild regularity conditions. Simulation results show that our proposed test can be tens or hundreds time faster than the FLUTE test by Hu et al. (2020) which uses a U-statistic of order four. We further demonstrate the superiority of our test by two real data applications. • A new statistic for testing functional linear model is constructed. • The new method achieves better performance especially for small/moderate data sets. • The asymptotic distribution of the proposed test is normal under some mild conditions. [ABSTRACT FROM AUTHOR]

Several tests for multivariate mean vector have been proposed in the recent literature. Generally, these tests are directly concerned with the mean vector of a high-dimensional distribution. The paper presents two new test procedures for testing mean vector in large dimension and small samples. We do not focus on the mean vector directly, which is a different framework from the existing choices. The first test procedure is based on the asymptotic distribution of the test statistic, where the dimension increases with the sample size. The second test procedure is based on the permutation distribution of the test statistic, where the sample size is fixed and the dimension grows to infinity. Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature. [ABSTRACT FROM AUTHOR]

I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify and fit a parametric network formation model, I introduce a new method based on matching pairs of agents with similar columns of the squared adjacency matrix, the ijth entry of which contains the number of other agents linked to both agents i and j. The intuition behind this approach is that for a large class of network formation models the columns of the squared adjacency matrix characterize all of the identifiable information about individual linking behavior. In this paper, I describe the model, formalize this intuition, and provide consistent estimators for the parameters of the regression model. [ABSTRACT FROM AUTHOR]

The categorical Gini correlation is an alternative measure of dependence between categorical and numerical variables, which characterizes the independence of the variables. A non‐parametric test based on the categorical Gini correlation for the equality of K distributions is developed. By applying the jackknife empirical likelihood approach, the standard limiting chi‐squared distribution with degrees of freedom of K − 1 is established and is used to determine the critical value and p‐value of the test. Simulation studies show that the proposed method is competitive with existing methods in terms of power of the tests in most cases. The proposed method is illustrated in an application on a real dataset. [ABSTRACT FROM AUTHOR]

A nonparametric test for equality of K variances has been proposed by developing the jackknife empirical likelihood ratio. The standard limiting Chi-squared distribution with degrees freedom of K - 1 for the test statistic is established, and is used to determine the type I error rate and the power of the test. Simulation studies have been conducted to show that the proposed method is competitive to the current existing methods, Levene's test and Fligner-Killeen's test, in terms of power and robustness. The proposed method has been illustrated in an application on a real data set. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of variance estimation of cross-validation. We consider the unbiased cross-validation risk estimate in the form of a general U-statistic and focus on estimating the variance of the U-statistic risk score. We propose an efficient variance estimator under a half-sampling design where the bias of the estimator can be expressed explicitly. Furthermore, we discuss a practical approach to estimate its bias by a two-layer Monte Carlo method so as to obtain a bias-corrected variance estimator. In the simulation study and real data examples, we evaluate the performance of the proposed variance estimator, in comparison to the commonly used bootstrap and jackknife methods, in the context of model selection under the one-standard-error rule. The numerical results suggest that the proposal yields identical or similar conclusion for model selection compared to its counterparts. Moreover, the developed variance estimator is much more efficient to calculate than its competitors. In the end, we discuss the generalization of the methodology to other partition-sampling scenarios. [ABSTRACT FROM AUTHOR]

In life testing situations, the residual life time of a component which has survived t units of time is Xt = X −t|X > t. In this paper, we give a central limit theorem result for the estimator of Var(Xt), the variance residual life(VRL) function. The result is used to construct normal approximation based confidence interval for the VRL. Furthermore, we use the jackknife empirical likelihood ratio procedure to obtain confidence interval for the VRL function. These intervals are compared through simulation study in terms of the average length and coverage probability. Finally, a numerical example illustrating the theory is also given.

In this paper, we propose a new test on the linear combinations of covariance matrices in high-dimensional data. Our statistic can be applied to many hypothesis tests on covariance matrices. In particular, the test proposed by Li and Chen (Ann Stat 40:908–940, 2012) on the homogeneity of two population covariance matrices is a special case of our test. The results are illustrated by an empirical example in financial portfolio allocation. [ABSTRACT FROM AUTHOR]

The area under the ROC (receiver operating characteristic) curve, AUC, is one of the most commonly used measures to evaluate the performance of a binary classifier. Due to sampling variation, the model with the largest observed AUC score is not necessarily optimal, so it is crucial to assess the variation of AUC estimate. We extend the proposal by Wang and Lindsay and devise an unbiased variance estimator of AUC estimate that is of a two‐sample U‐statistic form. The proposal can be easily generalized to estimate the variance of a K‐sample U‐statistic (K ≥ 2). To make our developed variance estimator more applicable, we employ a partition‐resampling scheme that is computationally efficient. Simulation studies suggest that the developed AUC variance estimator yields much better or comparable performance to jackknife and bootstrap variance estimators, and computational times that are about 10 to 30 times faster than the times of its counterparts. In practice, the proposal can be used in the one‐standard‐error rule for model selection, or to construct an asymptotic confidence interval of AUC in binary classification. In addition to conducting simulation studies, we illustrate its practical applications using two real datasets in medical sciences. [ABSTRACT FROM AUTHOR]

Variable screening for censored survival data is most challenging when both survival and censoring times are correlated with an ultrahigh‐dimensional vector of covariates. Existing approaches to handling censoring often make use of inverse probability weighting by assuming independent censoring with both survival time and covariates. This is a convenient but rather restrictive assumption which may be unmet in real applications, especially when the censoring mechanism is complex and the number of covariates is large. To accommodate heterogeneous (covariate‐dependent) censoring that is often present in high‐dimensional survival data, we propose a Gehan‐type rank screening method to select features that are relevant to the survival time. The method is invariant to monotone transformations of the response and of the predictors, and works robustly for a general class of survival models. We establish the sure screening property of the proposed methodology. Simulation studies and a lymphoma data analysis demonstrate its favorable performance and practical utility. [ABSTRACT FROM AUTHOR]

Inspired by the correlation matrix and based on the generalized Spearman's ρ and Kendall's τ between random variables proposed in Lu et al. (J Nonparametr Stat 30(4):860–883, 2018), ρ -matrix and τ -matrix are suggested for multivariate data sets. The matrices are used to construct the ρ -measure and the τ -measure among random vectors with statistical estimation and the asymptotic distributions under the null hypothesis of independence that produce the nonparametric tests of independence for multiple vectors. Simulation results demonstrate that the proposed tests are powerful under different grouping of the investigated random vector. An empirical application to detecting dependence of the closing price of a portfolio of stocks in NASDAQ also illustrates the applicability and effectiveness of our provided tests. Meanwhile, the corresponding measures are applied to characterize strength of interdependence of that portfolio of stocks during the recent two years. [ABSTRACT FROM AUTHOR]

This article proposes a nonparametric test for structural changes in linear regression models that allows for serial correlation, autoregressive conditional heteroskedasticity and time-varying variance in error terms. The test requires no trimming of the boundary region near the end points of the sample period, and requires no prior information on the alternative, what it requires is the transformed OLS residuals under the null hypothesis. We show that the test has a limiting standard normal distribution under the null hypothesis, and is powerful against single break, multiple breaks and smooth structural changes. The Monte Carlo experiment is conducted to highlight the merits of the proposed test relative to other popular tests for structural changes. [ABSTRACT FROM AUTHOR]

In many applications it is important to know whether the amount of fluctuation in a series of observations changes over time. In this article, we investigate different tests for detecting changes in the scale of mean-stationary time series. The classical approach, based on the CUSUM test applied to the squared centered observations, is very vulnerable to outliers and impractical for heavy-tailed data, which leads us to contemplate test statistics based on alternative, less outlier-sensitive scale estimators. It turns out that the tests based on Gini's mean difference (the average of all pairwise distances) and generalized Qn estimators (sample quantiles of all pairwise distances) are very suitable candidates. They improve upon the classical test not only under heavy tails or in the presence of outliers, but also under normality. We use recent results on the process convergence of U-statistics and U-quantiles for dependent sequences to derive the limiting distribution of the test statistics and propose estimators for the long-run variance. We show the consistency of the tests and demonstrate the applicability of the new change-point detection methods at two real-life data examples from hydrology and finance. for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a new nonparametric conditional mean independence test for a response variable |$Y$| and a predictor variable |$X$| where either or both can be function-valued. Our test is built on a new metric, the so-called functional martingale difference divergence, which fully characterizes the conditional mean dependence of |$Y$| given |$X$| and extends the martingale difference divergence proposed by Shao & Zhang (2014). We define an unbiased estimator of functional martingale difference divergence by using a |$\mathcal{U}$| -centring approach, and we obtain its limiting null distribution under mild assumptions. Since the limiting null distribution is not pivotal, we use the wild bootstrap method to estimate the critical value and show the consistency of the bootstrap test. Our test can detect the local alternative which approaches the null at the rate of |$n^{-1/2}$| with a nontrivial power, where |$n$| is the sample size. Unlike the three tests developed by Kokoszka et al. (2008) , Lei (2014) and Patilea et al. (2016) , our test does not require a finite-dimensional projection or assume a linear model, and it does not involve any tuning parameters. Promising finite-sample performance is demonstrated via simulations, and a real-data illustration is used to compare our test with existing ones. [ABSTRACT FROM AUTHOR]

This article investigates slow-explosive AR(1) processes, which converge to a random walk (RW) process with logarithm rates, to fill the gap between nearly non-stationary AR(1) and moderately deviated AR(1) processes, and derives the asymptotics of the least squares estimator using central limit theorems for (reduced) U-statistic. We successfully establish the smooth link between the nearly non-stationary AR(1) and the moderately deviated AR(1) processes. Some novel results are reported, which include the convergence of the least squares estimator to a biased fractional Brownian motion. [ABSTRACT FROM AUTHOR]

This paper proposes a nonparametric procedure for testing conditional quantile independence using projections. Relative to existing smoothed nonparametric tests, the resulting test statistic: (i) detects the high frequency local alternatives that converge to the null hypothesis in probability at faster rate and, (ii) yields improvements in the finite sample power when a large number of variables are included under the alternative. In addition, it allows the researcher to include qualitative information and, if desired, direct the test against specific subsets of alternatives without imposing any functional form on them. We use the weighted Nadaraya-Watson (WNW) estimator of the conditional quantile function avoiding the boundary problems in estimation and testing and prove weak uniform consistency (with rate) of the WNW estimator for absolutely regular processes. The procedure is applied to a study of risk spillovers among the banks. We show that the methodology generalizes some of the recently proposed measures of systemic risk and we use the quantile framework to assess the intensity of risk spillovers among individual financial institutions. [ABSTRACT FROM AUTHOR]