Testing Regression Coefficients in High-Dimensional and Sparse Settings

In the high-dimensional setting, this article considers a canonical testing problem in multivariate analysis, namely testing coefficients in linear regression models. Several tests for highdimensional regression coefficients have been proposed in the recent literature. However, these tests are based on the sum of squares type statistics, that perform well under the dense alternatives and suffer from low power under the sparse alternatives. In order to attack this issue, we introduce a new test statistic which is based on the maximum type statistic and magnifies the sparse signals. The limiting null distribution of the test statistic is shown to be the extreme value distribution of type I and the power of the test is analysed. In particular, it is shown theoretically and numerically that the test is powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature.     

A Score Type Test for General Autoregressive Models in Time Series

This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.     

A note on scale estimates based on the empirical characteristic function and their application to test for normality

We present a test for the composite hypothesis of normality against general alternatives. The test statistic is essentially the difference of two estimates of scale based on the empirical characteristic function. The test is simple to apply and its performance is comparable with that of several other well-known tests of normality.     

TESTING THE ADEQUACY OF GARCH-TYPE MODELS IN TIME SERIES

In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.     

Regression type tests for parametric hypotheses based on optimally selected subsets of the order statistics

Through use of a regression framework, a general technique is developed for determining test procedures based on subsets of the order statistics for both simple and composite parametric null hypotheses. Under both the null hypothesis and sequences of local alternatives these procedures are asymptotically equivalent in distribution to the generalized likelihood ratio statistic based on the corresponding order statistics. A simple, approximate method for selecting quantiles for such tests, which endows the corresponding test statistics with optimal power properties, is also given.     

完全区组设计下基于Aligned秩的有方向检验问题

本文基于Aligned秩给出了用于解完全区组设计有方向检验问题的, 我们称之为$C$-检验的检验方法. 本文分别对每个试验单元仅有一个观测值以及等重复观测值和不等重复观测值各种情形下的$C$检验进行了讨论, 并在原假设$H_0$成立时计算了上述各种情形下$C$检验统计量的数学期望和方差, 且证明了$C$检验统计量的渐近分布为正态分布.     

半参数广义线性模型的影响分析与异常点检验

统计诊断就是对统计推断方法解决问题的全过程进行诊断，而影响分析是统计诊断中十分重要的分支．本文针对半参数广义线性模型，证明了数据删除模型和均值漂移模型的等价性定理，给出了诸如广义Cook距离等诊断统计量并研究了异常点的Score检验统计量，最后通过实例验证了本文给出的诊断方法的有效性。     

面板数据交互固定效应模型的方差分量检验

研究了面板数据交互固定效应模型中方差分量的检验问题.首先依据模型中误差项的估计构造辅助回归模型,然后根据该辅助回归构造检验统计量,对模型中的异方差性进行检验.进一步,通过构造不同的辅助回归模型和检验统计量可以判别异方差的来源.在一定正则条件下,得到了检验统计量在原假设和备择假设下的渐近分布,并说明所提出的检验方法不依赖于误差分布.最后,通过模拟研究对本文的检验方法进行评价,说明所提检验方法是有效的.     

Assessing the Error Probability of the Model Selection Test

The asymptotic error probability of Linhart's model selection test isevaluated, and compared with the nominal significance level. We examine thecase where the expected discrepancies of the candidate models from the truemodel are asymptotically equal. The local alternatives method is employed inthe limiting operation of the asymptotic evaluation. Although the errorprobability under the null hypothesis is actually shown to be equal to orless than the level for most situations, intolerable violations of the errorcontrol are observed for nested models: It is often erroneously concludedthat the smaller model is significantly better than the larger model. Toprevent this violation, a modification of Linhart's test statistic isproposed. The effectiveness of the proposed test is confirmed throughtheoretical analysis and numerical simulations.     

Goodness-of-fit tests for vector autoregressive models in time series

The paper proposes and studies some diagnostic tools for checking the goodness-of-fit of general parametric vector autoregressive models in time series. The resulted tests are asymptotically chi-squared under the null hypothesis and can detect the alternatives converging to the null at a parametric rate. The tests involve weight functions,which provides us with the flexibility to choose scores for enhancing power performance,especially under directional alternatives. When the alternatives are not directiona...     

Two-Stage Likelihood Ratio and Union–Intersection Tests for One-Sided Alternatives Multivariate Mean with Nuisance Dispersion Matrix

For a multinormal distribution with an unknown dispersion matrix, union-intersection (UI) tests for the mean against one-sided alternatives are considered. The null distribution of the UI test statistic is derived and its power monotonicity properties are studied. A Stain-type two-stage procedure is proposed to eliminate some of the inherent drawbacks of such tests. Some comparisons are also made with some recently proposed alternative conditional likelihood ratio tests.     

Power maps in goodness-of-fit testing

For classical goodness-of-fit tests as well as for their modified versions in case of Type-II right censored data, results of a simulation study are presented, where the powers of the tests under consideration against beta alternatives are illustrated in informative, user-oriented plots that offer the possibility to directly choose the best test statistic in a concrete situation, when some prior belief about the alternative is available. The behavior of powers of respective statistical tests as functions of beta parameters is examined and discussed.     

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.     

半参数广义线性随机效应模型的影响分析

该文系统研究了半参数广义线性随机效应模型的统计诊断与影响分析方法, 证明了数据删除模型和均值漂移模型的等价性定理, 给出了广义Cook距离等诊断统计量及异常点的Score检验统计量并研究了该模型的局部影响分析,分别对加权扰动模型, 响应变量扰动模型得到了影响距阵的计算公式, 最后通过一个实例验证了文中给出诊断方法的有效性.     

Some Simple Test Procedures for Normal Mean Vector with Incomplete Data

The problem of testing normal mean vector when the observations are missing from subsets of components is considered. For a data matrix with a monotone pattern, three simple exact tests are proposed as alternatives to the traditional likelihood ratio test. Numerical power comparisons between the proposed tests and the likelihood ratio test suggest that one of the proposed tests is indeed comparable to the likelihood ratio test and the other two tests perform better than the likelihood ratio test over a part of the parameter space. The results are extended to a nonmonotone pattern and illustrated using an example.     

A Data Driven Smooth Test for Circular Uniformity

We propose a new omnibus test for uniformity on the circle. The new test is based upon the idea of data driven smooth tests as presented in Ledwina (1994, J. Amer. Statist. Assoc., 89, 1000–1005). Our simulations indicate that the test performs very well for multifarious alternatives. In particular, it seems to outperform other known omnibus tests when testing against multimodal alternatives. We also investigate asymptotic properties of our test and we prove that it is consistent against every departure from uniformity.     

线性模型中M检验原假设分布的随机加权逼近

在线性模型中M-方法可以用于线性假设检验, 其中M检验、Wald检验和Rao的计分型检验是最常用的检验准则. 但是在计算这些检验的临界值时都涉及到未知参数的估计. 在本文中我们利用随机加权的方法来逼近这些检验的原假设分布. 结果表明在原假设和局部对立假设之下随机加权统计量的渐近分布与原检验统计量在原假设之下的渐近分布相同. 因此我们不需要对冗余参数进行估计,利用随机加权的方法就可以得到这些检验的临界值. 而且在局部对立假设之下可以实现对功效的计算. 当取不同的误差分布和不同的随机权时, 我们对本文的方法进行了蒙特卡洛模拟. 结果表明用随机加权方法来逼近原假设分布是非常精确的.     

Locally optimal rank tests for independence

The problem of testing the hypothesis of independence against multiparametrical set of alternatives is considered. Rank tests, having some locally maximin property are studied and a certain characterization of these tests is given. Finite sample and asymptotic test statistics in a restricted class of tests are derived.     

Empirical likelihood ratio tests for multivariate regression models

This paper proposes some diagnostic tools for checking the adequacy of multivariate regression models including classical regression and time series autoregression. In statistical inference, the empirical likelihood ratio method has been well known to be a powerful tool for constructing test and confidence region. For model checking, however, the naive empirical likelihood (EL) based tests are not of Wilks’ phenomenon. Hence, we make use of bias correction to construct the EL-based score tests and derive a nonparametric version of Wilks’ theorem. Moreover, by the advantages of both the EL and score test method, the EL-based score tests share many desirable features as follows: They are self-scale invariant and can detect the alternatives that converge to the null at rate n ^−1/2, the possibly fastest rate for lack-of-fit testing; they involve weight functions, which provides us with the flexibility to choose scores for improving power performance, especially under directional alternatives. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of possible alternatives. A simulation study is carried out and an application for a real dataset is analyzed.      

Probability plots and order statistics of the standard extreme value distribution

A comparison between the ordinary least-squares estimator and the weighted least-squares estimator when the data set arises from the standard extreme value distribution is provided. Probability plot of the extreme value distribution is applied. A goodness-of-fit test of the standard extreme value distribution is introduced. The percentage points of the test statistic are investigated. The results of power study for the test statistic under various alternatives show that in most situations the proposed test statistic serves as well as do competing alternatives.