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.     

A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances

This article considers the twin problems of testing for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH disturbances in the linear regression model. A feature of these testing problems, ignored by the standard Lagrange multiplier test, is that they are onesided in nature. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The small-sample-size and power properties of two versions of this test under both normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both versions of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.     

Smooth Tests of Copula Specifications

We present a family of smooth tests for the goodness of fit of semiparametric multivariate copula models. The proposed tests are distribution free and can be easily implemented. They are diagnostic and constructive in the sense that when a null distribution is rejected, the test provides useful pointers to alternative copula distributions. We then propose a method of copula density construction, which can be viewed as a multivariate extension of Efron and Tibshirani. We further generalize our methods to the semiparametric copula-based multivariate dynamic models. We report extensive Monte Carlo simulations and three empirical examples to illustrate the effectiveness and usefulness of our method.     

Seasonality Tests

This article modifies and extends the test against nonstationary stochastic seasonality proposed by Canova and Hansen. A simplified form of the test statistic in which the nonparametric correction for serial correlation is based on estimates of the spectrum at the seasonal frequencies is considered and shown to have the same asymptotic distribution as the original formulation. Under the null hypothesis, the distribution of the seasonality test statistics is not affected by the inclusion of trends, even when modified to allow for structural breaks, or by the inclusion of regressors with nonseasonal unit roots. A parametric version of the test is proposed, and its performance is compared with that of the nonparametric test using Monte Carlo experiments. A test that allows for breaks in the seasonal pattern is then derived. It is shown that its asymptotic distribution is independent of the break point, and its use is illustrated with a series on U.K. marriages. A general test against any form of permanent seasonality, deterministic or stochastic, is suggested and compared with a Wald test for the significance of fixed seasonal dummies. It is noted that tests constructed in a similar way can be used to detect trading-day effects. An appealing feature of the proposed test statistics is that under the null hypothesis, they all have asymptotic distributions belonging to the Cramér–von Mises family.     

Goodness of exact experimental designs with respect to a certain family of criteria

In the paper we assume to be given an approximate optimum exact design with respect to one optimality criterion. We investigate the goodness of this design in the sense of a family of criteria that includes those of A-E-, and .D-optimality.     

Pooling means under uncertain prior information with application to discrete distributions

The problem of pooling means is considered based on two samples in presence of the uncertain prior information that these samples are taken from possibly identical populations. Two discrete models, Poisson and binomial are considered in particular. Three estimators, i.e. the unrestricted estimator, shrinkage restricted estimator and estimators based on preliminary test are proposed. Their asymptotic mean squared errors are derived and compared. It is demonstrated via asymptotic results that the range of the parameter space in which shrinkage preliminary test estimator dominates the unrestricted estimator is wider than that of the usual preliminary test estimator. A Monte Carlo study for Poisson model is presented to compare the performance of the estimators for small samples.     

Inferring gene regulatory networks by an order independent algorithm using incomplete data sets

Analyzing incomplete data for inferring the structure of gene regulatory networks (GRNs) is a challenging task in bioinformatic. Bayesian network can be successfully used in this field. k-nearest neighbor, singular value decomposition (SVD)-based and multiple imputation by chained equations are three fundamental imputation methods to deal with missing values. Path consistency (PC) algorithm based on conditional mutual information (PCA–CMI) is a famous algorithm for inferring GRNs. This algorithm needs the data set to be complete. However, the problem is that PCA–CMI is not a stable algorithm and when applied on permuted gene orders, different networks are obtained. We propose an order independent algorithm, PCA–CMI–OI, for inferring GRNs. After imputation of missing data, the performances of PCA–CMI and PCA–CMI–OI are compared. Results show that networks constructed from data imputed by the SVD-based method and PCA–CMI–OI algorithm outperform other imputation methods and PCA–CMI. An undirected or partially directed network is resulted by PC-based algorithms. Mutual information test (MIT) score, which can deal with discrete data, is one of the famous methods for directing the edges of resulted networks. We also propose a new score, ConMIT, which is appropriate for analyzing continuous data. Results shows that the precision of directing the edges of skeleton is improved by applying the ConMIT score.     

Using the dependent wild bootstrap for the nonparametric goodness-of-fit test for density functions

In this paper, we consider the well-known nonparametric consistent model-specification test for the stationary density function (see [Aït-Sahalia Y. Testing continuous-time models of the spot interest rate. Rev Financ Stud. 1996;9:385–426; Li Q. Nonparametric testing of closeness between two unknown distribution functions. Econ Rev. 1996;15:261–274; Fan Y, Ullah A. On goodness-of-fit tests for weakly dependent processes using kernel method. J Nonparametric Stat. 2000;11:337–360]) and reinvestigate it carefully using asymptotics and simulation. Our work reveals that the test is subject to power and size distortions, which are mainly caused by dependence or convergence rate changes under the null and alternative hypothesis. A dependent wild bootstrap is newly suggested as a feasible remedy to such distortions. Our result provides a complete explanation as well as a solution to the problem that experienced by Aït-Sahalia [Testing continuous-time models of the spot interest rate. Rev Financ Stud. 1996;9:385–426], that is, that the test rejects true models too often when independent and identically distributed asymptotic critical values are used.     

Simplified Likelihood Based Goodness-of-fit Tests for the Weibull Distribution

The aim of this paper is to present new likelihood based goodness-of-fit tests for the two-parameter Weibull distribution. These tests consist in nesting the Weibull distribution in three-parameter generalized Weibull families and testing the value of the third parameter by using the Wald, score, and likelihood ratio procedures. We simplify the usual likelihood based tests by getting rid of the nuisance parameters, using three estimation methods. The proposed tests are not asymptotic. A comprehensive comparison study is presented. Among a large range of possible GOF tests, the best ones are identified. The results depend strongly on the shape of the underlying hazard rate.