Improvements in the Bias and Precision of Sample Quartiles
作者:
Govind S. Mudholkara,
Alan D. Hutson,
期刊:
Statistics
(Taylor Available online 1997)
卷期:
Volume 30,
issue 3
页码: 239-257
ISSN:0233-1888
年代: 1997
DOI:10.1080/02331889708802612
出版商: Gordon & Breach Science Publishers
关键词: Primary 62G30;62G20;Secondary 62F12;Asymptotic expansions;bias-variance tradeoff
数据来源: Taylor
摘要:
The sample quartiles, which are common in robust inference and nonparametric statistics, have many prevailing definitions, all with the same asymptotic distribution. In this note we examine the higher order terms in the asymptotic expansions for the bias, variance and M.S.E. of the commonly used quartiles, defined as the linear interpolant of two adjacent order statistics. The expansions are used to develop simple improvements of the interpolation based definition by removing theO(n-1) term in the bias and by minimizing the variance and M.S.E. up to orderO(n-2). It is noted that the variances of the traditional quartiles, instead of decreasing monotonically as the sample size increases, exhibit a periodic behavior. This is analogous to a property of sample medians observed by Hodges (1967), and discussed by Hodges and Lehmann (1967).
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