Testing Heterogeneity for Frailty Distribution in Shared Frailty Model

Abstract

The frailties, representing extra variations due to unobserved measurements, are often assumed to be iid in shared frailty models. In medical applications, however, a speculation can arise that a data set might violate the iid assumption. In this paper we investigate this conjecture through an analysis of the kidney infection data in McGilchrist and Aisbett (McGilchrist, C. A., Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466). As a test procedure, we consider the cusum of squares test which is frequently used for monitoring a variance change in statistical models. Our result strongly sustains the heterogeneity of the frailty distribution.     

IDENTIFYING THE OUT OF CONTROL VARIABLE IN A MULTIVARIATE CONTROL CHART

ABSTRACT

The identification of the out of control variable, or variables, after a multivariate control chart signals, is an appealing subject for many researchers in the last years. In this paper we propose a new method for approaching this problem based on principal components analysis. Theoretical control limits are derived and a detailed investigation of the properties and the limitations of the new method is given. A graphical technique which can be applied in some of these limiting situations is also provided.     

The Cucconi Test for Location-scale Alternatives in Application to Asymmetric Hydrological Variables

To identify location-scale trends, which environmental data often exhibit, location-scale tests have to be addressed. The aim of this article was to estimate size and power of the Cucconi rank-based test when applied to various skewed distributions, typical in hydrology. Results of the Monte Carlo simulation revealed great power for series with low coefficient of variation, time of change close to the middle, not very heavy tail, and with length of at least 60. Comparison to the Lepage test discovered larger usefulness of the Cucconi test for short series and change close to the middle. Several practical applications were presented.     

Testing equality of two normal means using combined samples of paired and unpaired data

A test for equality of two normal means when the data consist of both paired and unpaired observations is proposed. The proposed test is compared with two other standard methods known in the literature with respect to the type I error rate and power using simulation results.     

Empirical assessment of the applicability of shrinkage predictors in regression when past and future data differ

Jones and Copas (1986) present theoretical and simulation results on the relative merits of a Stein predictor (Copas, 1983) and the ordinary least squares predictor in the usual linear multiple regression model, when certain distributional properties of the regressor variables arising in the past differ from those for which predictions are to be made. Here, extension is made to the practical situation where the true regression parameters are unknown. A hypothesis testing procedure is developed to help determine which of shrinkage and least squares is preferable in any given instance. This approach is applied to explain some empirical evidence on the comparative merits of the two procedures, recently given by Berk (1984).     

Extending the Barnard’s test to non-inferiority

In 1945, George Alfred Barnard presented an unconditional exact test to compare two independent proportions. Critical regions for this test, by construction accomplish the very useful property of being Barnard convex sets. Besides, there are empirical findings suggesting that Barnard’s test is the most generally powerful. For Barnard’s test, calculation of critical regions is complicated due that they are constructed in an iterative form until is obtained a test size, as close as possible to the nominal significance level and less than or equal to it. In this article we present an extension to non-inferiority of this very leading test. This extension was contructed for any dissimilarity measure and tables were constructed for the difference between proportions. Also we calculate the critical regions for this extended test for sample sizes less or equal than 30, nominal significance level 0.01, 0.025, 0.05, and 0.10 and for non-inferiority margins 0.05, 0.10, 0.15, and 0.20. Additionally, we computed test sizes for the mentioned configurations. To do this calculations, we have written a program in the R environment.     

我国股票市场贝塔系数的稳定性检验

贝塔系数是用于衡量证券市场系统风险的一个重要概念。通过对贝塔系数的估计,投资者可以预测证券未来的市场风险。但是,贝塔系数必须要用过去的数据来估计。所以,除非贝塔系数具有相对的稳定性,否则,它就无法作为证券市场未来系统风险性的无偏差估计。利用ＣＨＯＷ 检验方法对深圳交易所交易数据进行实证分析,结果表明,在我国证券市场上,无论是单个股票还是股票组合,贝塔系数都不具稳定性。这说明目前我国证券市场的市场风险是变动不定和难以预测的。     

Two-way ANOVA when the distribution of the error terms is skew t

In this article, we assume that the distribution of the error terms is skew t in two-way analysis of variance (ANOVA). Skew t distribution is very flexible for modeling the symmetric and the skew datasets, since it reduces to the well-known normal, skew normal, and Student's t distributions. We obtain the estimators of the model parameters by using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies. We also propose new test statistics based on these estimators for testing the equality of the treatment and the block means and also the interaction effect. The efficiencies of the ML and the MML estimators and the power values of the test statistics based on them are compared with the corresponding normal theory results via Monte Carlo simulation study. Simulation results show that the proposed methodologies are more preferable. We also show that the test statistics based on the ML estimators are more powerful than the test statistics based on the MML estimators as expected. However, power values of the test statistics based on the MML estimators are very close to the corresponding test statistics based on the ML estimators. At the end of the study, a real life example is given to show the implementation of the proposed methodologies.     

Modeling binary responses with stochastic covariates

In a traditional binary regression model, covariates are assumed to be fixed by design. In practice, however, they are most likely to be stochastic and non-normally distributed. We develop modified maximum likelihood estimators for such situations. We show that these estimators are more efficient than the traditional binary regression estimators and robust to data anomalies. We illustrate our results using a real life example.     

On testing uniformity using an information-theoretic measure

As a measure of certainty, informational energy has been used in many statistical problems. In this article, we introduce some estimators of this quantity by modifying the basic estimator available in the literature. The new measures are then used to develop tests of uniformity. A Monte Carlo simulation study is performed to evaluate power behavior of the proposed tests. The results confirm the preference of the new tests in some situations.