Title: Estimation of the Parameters of a Selected Multivariate Population

Author(s): Morteza Amini and Nader Nematollahi
Issue: Volume 79 Series A Part 1 Year 2017
Pages: 13 -- 38
The problem of estimation of the parameters of a selected univariate distribution has been studied extensively in the literature, in which a one dimensional random parameter is estimated using a random sample of one dimensional observations. There are situations where the selection process is performed using multiple variables or the selection of the population is done using an auxiliary variable. It is natural that such a random vector has a multivariate distribution with a multidimensional parameter space. In this paper, certain methods are developed for estimation of the multidimensional parameters of the selected multivariate distribution. The risks of the proposed estimators are estimated and certain sufficient conditions for inadmissibility of the estimators are given for two classes of the estimators. The results are applied to a prostate cancer data set to illustrate the applicability of theoretical results.
AMS (2000) subject classification . 62C07, 62F07, 62F10, 62H12.
Keywords and phrases: Auxiliary variable, Gamma distribution, Random parameter, Scale parameter, Uniformly minimum risk unbiased estimation.