Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

Document Type

Article

Publication Date

1-1-2016

Publication Title

Environmental and Ecological Statistics

Volume

23

Issue

2

First page number:

301

Last page number:

316

Abstract

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology. © 2016, Springer Science+Business Media New York.

Keywords

Concomitants of order statistics; Dirichlet process; Morgenstern family of distributions; Ranked set sampling; Ranking error; Semi-parametric Bayesian estimation

Language

English

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