Pitman closeness of sample median to population median. (English) Zbl 1169.62324

Summary: 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.


62G30 Order statistics; empirical distribution functions
62F10 Point estimation
Full Text: DOI


[1] Arnold, B.C.; Balakrishnan, N.; Nagaraja, H.N., A first course in order statistics, (2008), SIAM Philadelphia · Zbl 1172.62017
[2] Bose, S., Estimating the center of symmetry: Is it always better to use larger sample sizes?, J. statist. plann. inference, 136, 4194-4203, (2006) · Zbl 1097.62011
[3] David, H.A.; Nagaraja, H.N., Order statistics, (2003), John Wiley & Sons Hoboken, New Jersey · Zbl 0905.62055
[4] Ghosh, M.; Sen, P.K., Median unbiasedness and Pitman closeness, J. amer. statist. assoc., 84, 1089-1091, (1989) · Zbl 0702.62022
[5] Keating, J.P., Karlin’s corollary—A topological approach to pitman’s measure of closeness, Comm. statist. theory methods, 20, 3729-3750, (1991) · Zbl 0800.62119
[6] Keating, J.P.; Mason, R.L.; Sen, P.K., Pitman’s measure of closeness, (1993), SIAM Philadelphia · Zbl 0779.62019
[7] Rossa, A.; Zielinski, R.A., Simple improvement of the kaplan – meier estimator, Comm. statist. theory methods, 31, 147-158, (2002) · Zbl 0991.62082
[8] Sen, P.K., The Hajek convolution theorem and empirical Bayes estimation: parametrics, semiparametrics and nonparametrics, J. statist. plann. inference, 91, 541-556, (2000) · Zbl 0965.62004
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