Kernel Density Estimator From Ranked Set Samples

• Published in: Communications in statistics. Theory and methods Vol. 43; no. 10-12; pp. 2156 - 2168
• Main Authors: Lim, Johan, Chen, Min, Park, Sangun, Wang, Xinlei, Stokes, Lynne
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 15-05-2014; Taylor & Francis Ltd
• Subjects: 62G07; Asymptotic properties; Bandwidth; Density; Estimators; Kernel density estimator; Kernels; Optimal bandwidth; Ranked set sampling; Samples; Statistical analysis; Statistical methods
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2013.791372

We study kernel density estimator from the ranked set samples (RSS). In the kernel density estimator, the selection of the bandwidth gives strong influence on the resulting estimate. In this article, we consider several different choices of the bandwidth and compare their asymptotic mean integrated square errors (MISE). We also propose a plug-in estimator of the bandwidth to minimize the asymptotic MISE. We numerically compare the MISE of the proposed kernel estimator (having the plug-in bandwidth estimator) to its simple random sampling counterpart. We further propose two estimators for a symmetric distribution, and show that they outperform in MISE all other estimators not considering symmetry. We finally apply the methods in this article to analyzing the tree height data from Platt et al. (
1988
) and Chen et al. (
2003
).