A survey on multivariate chi-square distributions and their applications in testing multiple hypotheses

We are concerned with three different types of multivariate chi-square distributions. Their members play important roles as limiting distributions of vectors of test statistics in several applications of multiple hypotheses testing. We explain these applications and consider the computation of multiplicity-adjusted p-values under the respective global hypothesis. By means of numerical examples, we demonstrate how much gain in level exhaustion or, equivalently, power can be achieved with corresponding multivariate multiple tests compared with approaches which are only based on univariate marginal distributions and do not take the dependence structure among the test statistics into account. As a further contribution of independent value, we provide an overview of essentially all analytic formulas for computing multivariate chi-square probabilities of the considered types which are available up to present. These formulas were scattered in the previous literature and are presented here in a unified manner.     

Stationary bootstrapping for panel cointegration tests under cross-sectional dependence

Stationary bootstrapping is applied to panel cointegration tests which are based on the ordinary least-squares estimator and the seemingly unrelated regression (SUR) estimator of the residual unit root. Large sample validity of stationary bootstrapping is established. A finite sample experiment reveals that size performances of the bootstrap tests are much less sensitive to cross-sectional correlation than those of existing tests and a test based on the SUR estimator has substantially better power than existing tests.     

Goodness-of-fit tests for Pareto distribution based on a characterization and their asymptotics

In this paper we present a new characterization of the Pareto distribution and consider goodness-of-fit tests based on it. We provide an integral and Kolmogorov–Smirnov-type statistics based on U-statistics and we calculate Bahadur efficiency for various alternatives. We find locally optimal alternatives for those tests. For small sample sizes, we compare the power of those tests with some common goodness-of-fit tests.     

An Empirical Analysis of Some Nonparametric Goodness-of-Fit Tests for Censored Data

In this article, we consider some nonparametric goodness-of-fit tests for right censored samples, viz., the modified Kolmogorov, Cramer–von Mises–Smirnov, Anderson–Darling, and Nikulin–Rao–Robson χ² tests. We also consider an approach based on a transformation of the original censored sample to a complete one and the subsequent application of classical goodness-of-fit tests to the pseudo-complete sample. We then compare these tests in terms of power in the case of Type II censored data along with the power of the Neyman–Pearson test, and draw some conclusions. Finally, we present an illustrative example.     

Data Dependent Cells Chi‐Square Test With Recurrent Events

We consider a recurrent event wherein the inter‐event times are independent and identically distributed with a common absolutely continuous distribution function F. In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q‐dimensional parameter is unknown. We propose a general Chi‐squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi‐square estimator. Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures.     

A Nonparametric Test Procedure Based on Quantiles for the Right Censored Data

In this study, we propose nonparametric tests using the several quantile statistics simultaneously for the right censored data. First of all, we consider statistics of the quadratic form with estimated covariance matrices. Then we derive the limiting distribution using the large sample approximation theory. Also we consider different forms of statistics such as the maximal and summing types with their limiting distributions. Then we illustrate our procedure with examples and compare performance among tests with empirical powers through a simulation study. Also we comment briefly on some interesting features including re-sampling methods as concluding remarks. Finally in Appendices, we provide proofs for the theoretic results needed for the derivation of the limiting distributions of the proposed test statistics.     

Finite-sample Resampling-based Combined Hypothesis Tests,with Applications to Serial Correlation and Predictability

This article suggests Monte Carlo multiple test procedures which are provably valid in finite samples. These include combination methods originally proposed for independent statistics and further improvements which formalize statistical practice. We also adopt the Monte Carlo test method to noncontinuous combined statistics. The methods suggested are applied to test serial dependence and predictability. In particular, we introduce and analyze new procedures that account for endogenous lag selection. A simulation study illustrates the properties of the proposed methods. Results show that concrete and nonspurious power gains (over standard combination methods) can be achieved through the combined Monte Carlo test approach, and confirm arguments in favor of variance-ratio type criteria.     

大学英语四级完形填空的题型设计及应试技巧

阐述了完形填空题型的发展过程及其特点 ,深入分析了我国大学英语四级考试中完形填空的命题要求 ,并结合学生应试心理及命题特点 ,着重提出了一套相应的应试技巧。