Pitman closeness of sample median to population median

In this paper, Pitman closeness of order statistics to the median of a distribution is discussed. In particular, it is shown that the sample median is the Pitman-closest order statistic to the population median in some general situations, and expressions for probabilities of closeness are also deriv...

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Bibliographic Details
Published in:Statistics & probability letters 2009-08, Vol.79 (16), p.1759-1766
Main Authors: Balakrishnan, N., Iliopoulos, G., Keating, J.P., Mason, R.L.
Format: Article
Language:English
Subjects:
Distribution theory
Exact sciences and technology
General topics
Mathematics
Nonparametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
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Summary:In this paper, Pitman closeness of order statistics to the median of a distribution is discussed. In particular, it is shown that the sample median is the Pitman-closest order statistic to the population median in some general situations, and expressions for probabilities of closeness are also derived.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2009.04.016