Bayesian estimation based on trimmed samples from Pareto populations

Abstract

Trimmed samples are widely employed in several areas of statistical practice, especially when some sample values at either or both extremes might have been contaminated. The problem of estimating the inequality and precision parameters of a Pareto distribution based on a trimmed sample and prior information is considered. From an inferential viewpoint, the problem of finding the highest posterior density (HPD) estimates of the Pareto parameters is discussed. The existence and uniqueness of the HPD estimates are established under mild conditions; explicit and accurate lower and upper bounds are also provided. Adopting a decision-theoretic perspective, several Bayesian estimators for standard loss functions are presented. In addition, two-sided and HPD credibility intervals for each Pareto parameter and joint HPD credibility regions for both parameters are derived, which have the corresponding frequentist confidence level in the noninformative case. Finally, an illustrative example concerning annual wage data is included.