JOURNAL OF STATISTICAL SCIENCES
Year:2008 | Volume:1 | Issue:2|Papers Count:7

In this paper, we obtain the generalized least square, restricted generalized least square and shrinkage estimators for the regression vector parameter assuming that the errors have multivariate t distribution. Also we calculate their quadratic risks and propose the dominance order of the underlying estimators.

The estimate of entropy (sample entropy), has been introduced by Vasicek (1976), for the first time. In this paper, we provide an estimate of entropy of order statistics that is the extention of the entropy estimate. Then we present an application of the entropy estimate of order statistics as a test statistic for symmetry of distribution versus skewness. The proposed test has been compared with some other existing tests. A Monte Carlo simulation study shows that the proposed test has more power than the Park's.

In recent years, some statisticians have studied the signal detection problem by using the random field theory. In this paper we have considered point estimation of the Gaussian scale space random field parameters in the Bayesian approach. Since the posterior distribution for the parameters of interest does not have a closed form, we introduce the Markov Chain Monte Carlo (rv'ICrv'IC) algorithm to approximate the Bayesian estimations. vVc have also applied the proposed procedure to real flv'IRI data, collected by the Montreal Neurological Institute.

Modeling correlated ordinal response data is usually more complex than the case of continuous and binary responses. Existing literature lacks an appropriate approach to modeling such data. For small sample sizes, however) these models lose their appeal since their inferences arc based OIl large samples. In this work, the Bayesian analysis of an asymmetric bivariate ordinal latent variable model has been developed. The latent response variable has been chosen to follow the generalized bivariate Gumble distribution. Using some specific priors and MCMC algorithms the regression parameters were estimated. As an application, a data set concerning Diabetic Retinopathy in 116 patients have been analyzed. This data set includes the disease status of each eye for patients as an ordinal response and a number of explanatory variables some of which are common to both eyes and the rest are organ specific.

Recurrent events arc one type of the multivariate survival data. Correlation between observations OIl each subject is the most important feature of this type of data. This feature does not allow using the ordinary survival models. Frailty models arc one of the main approaches to the analysis of recurrent events. Ordinary Frailty models assumed the frailty is constant over time that is not realistic in many applications. In this paper we introduce a time-dependent frailty model. The introduced model is based on piecewise semi parametric proportional hazard and frailty variable followed a Gamma distribution. The frailty variable in the model has a gamma process that is constant during each interval and has independent increments in the beginning of each interval. vVe found a close form function for integrated likelihood function and estimated parameters of model. The efficiency of introduced model was compared with an ordinary constant gamma model by a simulation study.

In this paper, first spatial point processes and their characteristics arc briefly introduced. Then after defining the spatial Cox processes in general terms, a special subclass; that is shot noise Cox processes, arc investigated. Finally a Thomas process is fitted to the locations of Zagros earthquakes.