A monte carlo study on the robustness of the two-sample sequential t test

The robustness of the two-sample sequentla1 t test was studied against departures from normality and equality of variances The effect of skewness and kurtosis of the underlying distribution on the test 1s relatively mild but the effect of heteroscedasticity serious.     

C337. Misspecified location and scale. 11. independence of and s2

A hierarchical Bayesian approach to the problem of estimating the largest normal mean is considered. Calculation of the posterior mean and the posterior variance involves, at worst, 3-dimensional numerical integration, for which an efficient Monte Carlo method of evaluation is given. An example is presented to illustrate the methodology. In the two populations case, computation of the posterior estimates can be substantially simplified and in special cases can actually be performed using closed form solutions. A simulation study has been done to compare mean square errors of some hierarchical Bayesian estimators that are expressed in closed forms and several existing estimators of the larger mean.     

Test inversion bootstrap confidence intervals

In this paper we explore the theoretical and practical implications of using bootstrap test inversion to construct confidence intervals. In the presence of nuisance parameters, we show that the coverage error of such intervals is O ( n ^−1/2) which may be reduced to O ( n ⁻¹) if a Studentized statistic is used. We present three simulation studies and compare the performance of test inversion methods with established methods on the problem of estimating a confidence interval for the dose–response parameter in models of the Japanese atomic bomb survivors data.     

Alternative beta estimation for the market model using partially adaptive techniques

The leptokurtosls of many security market return distributions can contaminate ordinary least squares estimates of the β coefficient of the market model. Partially adaptive estimation techniques accommodate the possibility of fat tailed distributions. this methodology limits the influence of extremely large residuals and yields estimates which are both statistically and practically different from ordinary least squares.     

Identification of out of control quality characteristics in a multivariate manufacturing environment

There are many instances in which the quality of a product or constancy of a process is determined by the joint levels of several attributes or properties. During the conduct of such a process or the production of such a product, one wishes to detect as quickly as possible any departure from a satisfactory state, while at the same time identifying which attributes are responsible for the deviation. In most cases of practical interest, however, there exist correlations among the several properties of interest; this makes it advisable to monitor certain aggregate characteristics of the process, rather than observing its various components separately. When the mean vector of the quality attributes is the major concern, this aggregate monitoring function is most commonly implemented via a T ² chart. The dependencies among attributes, however, complicate the determination of which are responsible when a deviation occurs. This paper presents an approach to help identify aberrant variables when Shewhart type multivariate control charts based on Hotelling's T ² are in use.     

BINARY REGRESSION WITH A CLASS OF SKEWED t LINK MODELS

ABSTRACT

In this paper we propose a class of skewed t link models for analyzing binary response data with covariates. It is a class of asymmetric link models designed to improve the overall fit when commonly used symmetric links, such as the logit and probit links, do not provide the best fit available for a given binary response dataset. Introducing a skewed t distribution for the underlying latent variable, we develop the class of models. For the analysis of the models, a Bayesian and non-Bayesian methods are pursued using a Markov chain Monte Carlo (MCMC) sampling based approach. Necessary theories involved in modelling and computation are provided. Finally, a simulation study and a real data example are used to illustrate the proposed methodology.     

Characteristic function of the SGT distribution

An explicit closed form is derived for the characteristic function for the skew generalized t distribution studied by Arslan and Genç [The skew generalized t (SGT) distribution as the scale mixture of a skew exponential power distribution and its applications in robust estimation, Statistics 43(5) (2009), pp. 481–498]. The expression involves the Wright generalized hypergeometric Ψ–function.     

An Optimal Confidence Region for the Largest and the Smallest Means from a Multivariate Normal Distribution

An optimal confidence region is proposed for obtaining the largest and the smallest means of a multivariate normal distribution with a common unknown variance and a non-negative correlation coefficient. The confidence region is compared to a class of asymmetric confidence regions, and the results show that it is uniformly better. Further, a design-oriented two-stage confidence region with a fixed width is also given. Finally, the optimal confidence region is applied to an experiment to measure the treatment effectiveness of a physical therapy with four independent groups and the result reveals that the proposed confidence region can provide some useful information.     

The Effect of Estimation of Unknown Degrees of Freedom on Estimation of Remaining Parameters in Spanos’ Conditional t Heteroskedastic Model

This article investigates the effect of estimation of unknown degrees of freedom on efficient estimation of remaining parameters in Spanos’ conditional t heteroskedastic model. We compare by simulation three maximum likelihood estimators (MLEs) of the remaining parameters in the model: the MLE of the remaining parameters when all the parameters are estimated by the MLE, when the degrees of freedom is estimated by a method of moments estimator, and when the degrees of freedom is erroneously specified. The latter two methods are found to perform poorly compared to the former method for the inference of variance parameters in the model. Thus, efficient estimation of degrees of freedom by the MLE is important to estimate efficiently the remaining variance parameters.