This article is cited in 10 papers

Asymptotic expansions for median estimate of a parameter

M. V. Burnashev

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We obtain asymptotic expansions for the distribution of a median (of empirical distribution) estimate of a parameter in additive noise with symmetric density. For Laplacian (i.e., two-sided exponential) density this estimate coincides with the maximum likelihood estimate. As a corollary we obtain asymptotic expansions for moments of these estimates. Numerical comparisons with exact data show that the use of asymptotic expansions significantly increases the accuracy of statistical inferences even for relatively small sample sizes.

Keywords: median estimate, asymptotic expansions.

Received: 11.07.1995

DOI: 10.4213/tvp3193

 English version: Theory of Probability and its Applications, 1997, 41:4, 632–645

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