Moments of the function of non-normal random vector with applications to econometric estimators and test statistics

In this paper we have provided a general result on the moments of a function of nonnormal random vector. The results for the normal case follow as a special case of this result. It is also indicated that the moments of a large class of econometric estimators and test statistics can be obtained by using our general result. This includes least squares estimator in the dynamic model, unit root tests, and the two step semiparametric estimators, among others.     

The asymptotic distribution of the likelihood ratio when the model is incorrect

Classical results on the asymptotic distribution of the likelihood ratio statistic rely on the assumption that the model chosen to construct the test statistic be correct. The model is said to be correct if it contains the true distribution of the observations. In this paper the asymptotic distribution of the likelihood ratio statistic is derived without the condition that the model need be correct.     

On-line control procedures under the random-walk model with measurement error and attribute observations

Assuming the quality characteristic process follows the random-walk model, the economic online control procedures are investigated by using the boundary correction technique when (1) the noise or measurement error follows either the random-walk model or the pure random model, and (2) the observations are taken by attributes only. Simple approximations for the long-run cost rate and optimal-control parameters are obtained.     

A Comparison of Permutation Hotelling's T 2 Test and Log-Ratio Test for Analyzing Compositional Data

An adding-back model is constructed for studying multiple outliers and influential observations. A logarithmic functional form for some influence measures having a better justification for plotting purposes is suggested. Two graphical methods with contours of constant measure values are proposed. They provide valuable information about the interrelationship of multiple influential observations and influence measures.     

Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty Model

In this article, we consider shared frailty model with inverse Gaussian distribution as frailty distribution and log-logistic distribution (LLD) as baseline distribution for bivariate survival times. We fit this model to three real-life bivariate survival data sets. The problem of analyzing and estimating parameters of shared inverse Gaussian frailty is the interest of this article and then compare the results with shared gamma frailty model under the same baseline for considered three data sets. Data are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same group. The variance component estimation provides the estimated dispersion of the random effects. We carried out a test for frailty (or heterogeneity) using Bayes factor. Model comparison is made using information criteria and Bayes factor. We observed that the shared inverse Gaussian frailty model with LLD as baseline is the better fit for all three bivariate data sets.     

Subjective elicitation of hyperparameters of a conjugate Dirichlet prior and the corresponding Bayes analysis

Abstract

The paper elicits subjectively the Dirichlet prior hyperparameters based on the realistic opinion collected from the experts. The procedure used for subjective elicitation considers several stages such as the choice of experts, formation of some relevant questions to be asked to the experts for getting their opinion, pooling of opinion, quantification of information and then the formation of exact prior distribution through quantile assessment based on an iterative procedure. The resulting prior distribution is used to provide the Bayes analysis assuming multinomial sampling plan. The results are illustrated by means of a data set involving two life style factors of gallbladder carcinoma patients. The results convey the message that matches closely with the opinion given by the medical experts.     

Asymptotic Comparison of Two Discriminants Used in Normal Covariate Classification

In this paper, we examine the performance of Anderson's classification statistic with covariate adjustment in comparison with the usual Anderson's classification statistic without covariate adjustment in a two-population normal covariate classification problem. The same problem has been investigated using different methods of comparison by some authors. See the bibliography. The aim of this paper is to give a direct comparison based upon the asymptotic probabilities of misclassification. It is shown that for large equal sample size of a training sample from each population, Anderson's classification statistic with covariate adjustment and cut-off point equal to zero, has better performance.