一类相合的分位点型检验

广义非参数似然比检验统计量是一类很广的统计量,包含了众多重要的检验统计量,如Anderson-Darling(AD)等.利用Rubin的随机经验分布函数替代经验分布函数的方法,得到了广义非参数似然比检验统计量的新版本,构造了新的检验统计量.由于新的检验统计量在给定样本下仍然是随机变量,选择了它的分位点和期望作为检验统计量,分别称之为分位点型检验统计量和期望型检验统计量.在简单假设情况下,证明了分位点型检验统计量和期望型检验统计量在固定备择下的相合性.模拟结果显示,在某些备择下,新的检验的功效明显高于原有的基于经验分布函数的检验的功效.     

A generalized Hollander-Proschan type test for NBUE alternatives

In this note we develop a family of test statistics for testing exponentiality against NBUE alternatives. The asymptotic distribution of the test statistics is derived. The test statistics are shown to be asymptotically normal and consistent. This family of test statistics includes the test proposed by Hollander and Proschan (1975) as a special case. Efficiency studies have also been done.     

Compact Matrix Expressions for Generalized Wald Tests of Equality of Moment Vectors

Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test statistics are also considered for dealing with nonstandard conditions. The specialization will be carried out for testing the equality of multinomial populations, and the equality of variance and correlation matrices for both normal and nonnormal data. When testing the equality of correlation matrices, a scaled version of the normal theory chi-squared statistic is proven to be an asymptotically exact chi-squared statistic in the case of elliptical data.     

Diagnostic checking of multivariate nonlinear time series models with martingale difference errors

In this article, we derive the asymptotic distribution of residual autocovariance and autocorrelation matrices for a general class of multivariate nonlinear time series models by assuming only that the error term is a martingale difference sequence. Two types of applications are developed: global test statistics of the portmanteau type and one-lag test statistics, which describe the residual correlation at individual lags. To illustrate the proposed methodology, simulation results are reported for diagnosing multivariate threshold time series models. The following test statistics are compared: the classical test statistics presuming independent errors and the proposed methodology which supposes only martingale difference errors.     

椭球检验与统计量的渐近尾部性

In this paper,some test statistics of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.     

Tests of elliptical symmetry and the asymptotic tail behavior of the statistics

In this paper, some test statistics Of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.     

A constructive hypothesis test for the single-index models with two groups

Comparison of two-sample heteroscedastic single-index models, where both the scale and location functions are modeled as single-index models, is studied in this paper. We propose a test for checking the equality of single-index parameters when dimensions of covariates of the two samples are equal. Further, we propose two test statistics based on Kolmogorov–Smirnov and Cramér–von Mises type functionals. These statistics evaluate the difference of the empirical residual processes to test the equality of mean functions of two single-index models. Asymptotic distributions of estimators and test statistics are derived. The Kolmogorov–Smirnov and Cramér–von Mises test statistics can detect local alternatives that converge to the null hypothesis at a parametric convergence rate. To calculate the critical values of Kolmogorov–Smirnov and Cramér–von Mises test statistics, a bootstrap procedure is proposed. Simulation studies and an empirical study demonstrate the performance of the proposed procedures.     

Asymptotic normality of test statistics under alternative hypotheses

The aim of this paper is to present a framework for asymptotic analysis of likelihood ratio and minimum discrepancy test statistics. First order asymptotics are presented in a general framework under minimal regularity conditions and for not necessarily nested models. In particular, these asymptotics give sufficient and in a sense necessary conditions for asymptotic normality of test statistics under alternative hypotheses. Second order asymptotics, and their implications for bias corrections, are also discussed in a somewhat informal manner. As an example, asymptotics of test statistics in the analysis of covariance structures are discussed in detail.     

On the rate of convergence ofL- andR-statistics under alternatives

Asymptotic distributions of test statistics under alternatives are important from the point of view of their power properties. When the limiting distributions of test statistics are specified under the hypothesis in a certain sense, LeCam's third lemma ([4], Chapter 6) enables one to obtain their limiting distributions under close alternatives. In this paper we generalize LeCam's third lemma by using the rate of convergence in the case of asymptotically efficient test statistics. A general lemma is proved which is specified to linear combinations of order statistics (L-statistics) and linear rank statistics (R-statistics). Edgeworth-type asymptotic expansions for these statistics under alternatives are considered in [3]. Supported by the Russian Foundation for Fundamental Research (grant No. 93-01-01446). Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.     

ON SOME TESTS FOR ELLIPTICAL SYMMETRY

In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and any fixed alternative. The asymptotic properties of Bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on number theoretic method, is suggested.     

Testing for no effect in nonparametric regression via spline smoothing techniques

We propose three statistics for testing that a predictor variable has no effect on the response variable in regression analysis. The test statistics are integrals of squared derivatives of various orders of a periodic smoothing spline fit to the data. The large sample properties of the test statistics are investigated under the null hypothesis and sequences of local alternatives and a Monte Carlo study is conducted to assess finite sample power properties.     

Test for autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes

In this paper,we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes.For a test,we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations.It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge.The test statistics are evaluated by some empirical results.     

The empirical characteristic function and large sample hypothesis testing

The empirical characteristic function is considered as a tool for large sample testing of a hypothesis that can be characterized in terms of the characteristic function. Two test statistics based upon the empirical characteristic function are proposed. The limiting distributions of these test statistics are obtained and methods are suggested for using these limiting distributions to calculate critical regions.     

Power of edge exclusion tests for graphical log-linear models

Asymptotic multivariate normal approximations to the joint distributions of edge exclusion test statistics for saturated graphical log-linear models, with all variables binary, are derived. Non-signed and signed square-root versions of the likelihood ratio, Wald and score test statistics are considered. Non-central chi-squared approximations are also considered for the non-signed versions of the test statistics. Simulation results are used to assess the quality of the proposed approximations. These approximations are used to estimate the overall power of edge exclusion tests. Power calculations are illustrated using data on university admissions.     

On some testing problems for sparse contingency tables

A class of test statistics are proposed for sparse tables with ordered categories. It is shown that for different testing situations these test statistics asymptotically more powerful tests than Pearson's chi-square.     

A test for independence of two stationary infinite order autoregressive processes

This paper considers the independence test for two stationary infinite order autoregressive processes. For a test, we follow the empirical process method and construct the Cramér-von Mises type test statistics based on the least squares residuals. It is shown that the proposed test statistics behave asymptotically the same as those based on true errors. Simulation results are provided for illustration.     

含内生结构突变的STR模型检验及应用研究

文章研究了含内生结构突变的平滑转换(STR)模型的检验问题,依据特殊一一般一特殊的建模原则给出了检验过程及对应的检验统计量SupLM,Monte Carlo模拟表明各检验统计量的检验功效较高。文章提出的建模过程和检验统计量能检测出非线性和结构突变同时或者单独一种存在时的情形。结构突变或者非线性特征越明显,相应的检验统计量功效越高,相对而言,针对结构突变的检验功效高于非线性检验功效。最后,应用含结构突变的ESTR模型探讨了人民币对美元汇率的收益变化特征,发现新汇改以来汇率收益序列不单有结构突变,也存在非线性。     

Competitors of the Wilcoxon signed rank test

Summary Distribution-free statistics are proposed for one-sample location test, and are compared with the Wilcoxon signed rank test. It is shown that one of the statistics is superior to the Wilcoxon test in terms of approximate Bahadur efficiency. And we compare that statistic with the Wilcoxon test from the viewpoint of asymptotic expansion of power function under contiguous alternatives.     

A rank test based on the moments of order statistics of the modified Makeham distribution

Single moments of order statistics from the modified Makeham distribution (MMD) are derived, an identity about the single moments of order statistics is given, and the specific expected value and variance of the single moments of order statistics from the MMD are calculated. In this study, the order statistic from the MMD was applied to the rank sum test in a two-sample problem. The exact critical values of the designated statistics were evaluated. Simulations were used to investigate the power of these statistics for the two-sided alternative with several population distributions. The powers of the statistics were compared with the Wilcoxon rank sum statistic, the Lepage statistic, the modified Baumgartner statistic, the Savage test and the normal score test. The Edgeworth expansion was used to evaluate the upper tail probability for the preferred statistic, given finite sample sizes.     

非参数回归中方差变点的小波检测(英文)

本文主要研究了非参数回归模型中方差函数的变点, 利用小波方法构造的检验量来检测方差中的变点,建立了这些检验量的渐近分布, 并且运用这些检验量构造了方差变点的位置和跳跃幅度的估计, 给出了这些估计的渐近性质, 并进一步通过随机模拟验证了本文方法在有限样本下的性质.