Bayesian density estimation using ranked set samples

Abstract

AbstractIn this article, we present a Bayesian approach for estimating the underlying density using a ranked set sample. We assume that the observations are generated from a Dirichlet process mixture model. Density (as well as moments) of future values generated from the process are estimated through Markov chain Monte Carlo simulations. This approach extends earlier work on density estimation based on a Dirichlet process prior from a simple random sample to a ranked set sample. We carry out a simulation study using a normal kernel to compare the effect of using a simple random sample versus a ranked set sample on the predictive density. We show that the Bayesian density estimate resulting from a ranked set sample has a smaller average mean squared error than that from a simple random sample. Additionally, the average Kullback–Leibler distance of the density estimate based on the ranked set sample is shown to be closer to zero than that based on the corresponding simple random sample. We illustrate our method by applying it to shrub data available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.