The extended two-sample problem: nonparametric case

The classical two-sample problem is extended here to the case where the distribution functions of the observable random variables are specified functions of unknown distribution functions and the null hypotheses to be tested or the parameters to be estimated relate to these unknown distributions. Various properties of the proposed rank tests and derived estimates are studied.     

A Smooth Test in Proportional Hazard Survival Models Using Local Partial Likelihood Fitting

Proportional hazard models for survival data, even though popular and numerically handy, suffer from the restrictive assumption that covariate effects are constant over survival time. A number of tests have been proposed to check this assumption. This paper contributes to this area by employing local estimates allowing to fit hazard models in which covariate effects are smoothly varying with time. A formal test is derived to check for proportional hazards against smooth hazards as alternative. The test proves to possess omnibus power in that it is powerful against arbitrary but smooth alternatives. Comparative simulations and two data examples accompany the presentation. Extensions are provided to multiple covariate settings, where the focus of interest is to decide which of the covariate effects vary with time.     

Comparing Survival Times for Treatments with Those for a Control Under Proportional Hazards

Inferences for survival curves based on right censored data are studied for situations in which it is believed that the treatments have survival times at least as large as the control or at least as small as the control. Testing homogeneity with the appropriate order restricted alternative and testing the order restriction as the null hypothesis are considered. Under a proportional hazards model, the ordering on the survival curves corresponds to an ordering on the regression coefficients. Approximate likelihood methods, which are obtained by applying order restricted procedures to the estimates of the regression coefficients, and ordered analogues to the log rank test, which are based on the score statistics, are considered. Mau's (1988) test, which does not require proportional hazards, is extended to this ordering on the survival curves. Using Monte Carlo techniques, the type I error rates are found to be close to the nominal level and the powers of these tests are compared. Other order restrictions on the survival curves are discussed briefly.     

Distance Testing for Selecting the Best Population

Consider testing the null hypothesis that a given population has location parameter greater than or equal to the largest location parameter of k competing populations. This paper generalizes tests proposed by Gupta and Bartholomew by considering tests based on p -distances from the parameter estimate to the null parameter space. It is shown that all tests are equivalent when k →∞ for a class of distributions that includes the normal and the uniform. The paper proposes the use of adaptive quantiles. Under suitable assumptions the resulting tests are asymptotically equivalent to the uniformly most powerful test for the case that the location parameters of all but one of the populations are known. The increase in power obtained by using adaptive tests is confirmed by a simulation study.     

基于统计学变量筛选方法的心理测验题目的维度识别

近年来多维心理测验被广泛应用于各类评估,虽然编制测验时知道整个测验考察的潜在特质(或称为维度),但是测验题目具体考察的维度仍需确定。借助多维项目反应理论模型与广义线性模型的关系,使用LASSO和弹性网两种变量筛选方法,可解决测验题目的维度识别问题。模拟研究发现,LASSO方法比弹性网方法具有更好的维度识别效果,前者对不同类型的多维测验具有较高的维度识别准确率。     

Optimal Tests for No Contamination in Reliability Models

Inferences on mixtures of probability distributions, in general,and of life distributions, in particular, are receiving considerableimportance in recent years. The likelihood ratio procedure oftesting for the null hypothesis of no contamination is oftenvery cumbersome and lacks its usual asymptotic properties. Recently,SenGupta (1991) has introduced the notion of an `L-optimal' testfor such testing problems. The idea is to recast the originalseveral parametric hypotheses representation of the null hypothesisin terms of only a single hypothesis involving an appropriatelychosen parametric function. This approach is shown to be bothmathematically elegant and operationally simple for a quite generalclass of mixture distributions which contains, in particular,all mixtures of the one-parameter exponential family and alsoa very rich subclass of mixtures useful in life-testing and reliabilityanalysis. It is also illustrated through two examples—onebased on real-life data and the other on a simulated sample.     

Extremal dependence tests for contagion

A new test for financial market contagion based on changes in extremal dependence defined as co-kurtosis and co-volatility is developed to identify the propagation mechanism of shocks across international financial markets. The proposed approach captures changes in various aspects of the asset return relationships such as cross-market mean and skewness (co-kurtosis) as well as cross-market volatilities (co-volatility). Monte Carlo experiments show that the tests perform well except for when crisis periods are short in duration. Small crisis sample critical values are calculated for use in this case. In an empirical application involving the global financial crisis of 2008–2009, the results show that significant contagion effects are widespread from the US banking sector to global equity markets and banking sectors through either the co-kurtosis or the co-volatility channels, reinforcing that higher order moments matter during crises.     

Moments of nonparametric probability density functions of entropy estimators applied to testing the inverse Gaussian distribution

The inverse Gaussian (IG) distribution is widely used to model data and then it is important to develop efficient goodness of fit tests for this distribution. In this article, we introduce some new test statistics for examining the IG goodness of fit based on correcting moments of nonparametric probability density functions of entropy estimators. These tests are consistent against all alternatives. Critical points and power of the tests are explored by simulation. We show that the proposed tests are more powerful than competitor tests. Finally, the proposed tests are illustrated by real data examples.