Kernel Density Estimator From Ranked Set Samples

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...

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Vydáno v:Communications in statistics. Theory and methods Ročník 43; číslo 10-12; s. 2156 - 2168
Hlavní autoři: Lim, Johan, Chen, Min, Park, Sangun, Wang, Xinlei, Stokes, Lynne
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis 15.05.2014
Taylor & Francis Ltd
Témata:
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
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Shrnutí: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 ).
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ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2013.791372