On stochastic orders of absolute value of order statistics in symmetric distributions

Yaakov Malinovsky*, Yosef Rinott

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let Y1, ..., Yn be the order statistics of a simple random sample from a finite or infinite population, having median = M. We compare the variables | Yj - M | and | Ym - M |, where Ym is the sample median, that is, m = frac(n + 1, 2) for odd n. The comparison is in terms of the likelihood ratio order, which implies stochastic order as well as other orders. The results were motivated by the study of best invariant and minimax estimators for the k / N quantile of a finite population of size N, with a natural loss function of the type g (| FN (t) - frac(k, N) |), where FN is the population distribution function, t is an estimate, and g is an increasing function.

Original languageEnglish
Pages (from-to)2086-2091
Number of pages6
JournalStatistics and Probability Letters
Volume79
Issue number19
DOIs
StatePublished - 1 Oct 2009

Fingerprint

Dive into the research topics of 'On stochastic orders of absolute value of order statistics in symmetric distributions'. Together they form a unique fingerprint.

Cite this