Semi-parametric mixture models with ranked set samples

Abstract

Simple random sampling (SRS) is the common method in data collection. In many applications, measuring the variable of interest is costly, but ranking the units can be done easily. In these situations, one can use rank set sampling (RSS) to get more representative samples from the population. This thesis investigates the estimation of the semi-parametric finite mixture models (FMMs) with RSS. We develop a semiparametric version of the Expectation-Maximization (EM) algorithm to obtain the maximum likelihood (ML) estimate of the population with RSS data. We then propose the ML estimation of FMM with RSS data in a semi-parametric framework. Our numerical studies show that the proposed EM algorithm estimates more efficiently the FMM. The proposed methods are finally applied to analyze the bone mineral data.