Bayesian Statistical Inference on Elliptical Matrix Distributions
نویسندگان
چکیده
In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parameters + and 7. Under a noninformative prior distribution, we obtain the posterior distribution, posterior mean, and generalized maximim likelihood estimators of + and 7. Under the entropy loss and quadratic loss, the best Bayesian estimators of 7 are derived as well. Some applications are given. 1999 Academic Press AMS 1991 subject classifications: 62C10, 62F10, 62F15.
منابع مشابه
The Family of Scale-Mixture of Skew-Normal Distributions and Its Application in Bayesian Nonlinear Regression Models
In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently, the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed d...
متن کاملInference for the Proportional Hazards Family under Progressive Type-II Censoring
In this paper, the well-known proportional hazards model which includes several well-known lifetime distributions such as exponential,Pareto, Lomax, Burr type XII, and so on is considered. With both Bayesian and non-Bayesian approaches , we consider the estimation of parameters of interest based on progressively Type-II right censored samples. The Bayes estimates are obtained based on symmetric...
متن کاملBayesian Estimation of Parameters in the Exponentiated Gumbel Distribution
Abstract: The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. In this paper, we estimate the EG's parameters in the Bayesian framework. We consider a 2-level hierarchical structure for prior distribution. As the posterior distributions do not admit a closed form, we do an approximated inference by using ...
متن کاملThe joint distribution of Studentized residuals under elliptical distributions
Scaled and Studentized statistics are encountered frequently, and they often play a decisive role in statistical inference and testing. For instance, taking the sample mean vector X̄ = ∑N j=1 Xj/N and the sample covariance matrix S = ∑N j=1(Xj − X̄)(Xj − X̄)/(N − 1) for an iid sample {Xj}j=1, some statistics for testing normality of the underlying distribution consist of the scaled residuals (the ...
متن کاملElicited Data and Incorporation of Expert Opinion for Statistical Inference in Spatial Studies1
Spatial data are often sparse by nature. However, in many instances, information may exist in the form of “soft” data, such as expert opinion. Scientists in the field often have a good understanding of the phenomenon under study and may be able to provide valuable information on its likely behavior. It is thus useful to have a sensible mechanism that incorporates expert opinion in inference. Th...
متن کامل