A Berry-Esseen Theorem for Linear Combinations of Order Statistics

R. Helmers

doi:10.1214/aop/1176994478

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Home > Journals > Ann. Probab. > Volume 9 > Issue 2 > Article

April, 1981 A Berry-Esseen Theorem for Linear Combinations of Order Statistics

R. Helmers

Ann. Probab. 9(2): 342-347 (April, 1981). DOI: 10.1214/aop/1176994478

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Abstract

A Berry-Esseen bound of order $n^{-1/2}$ is established for linear combinations of order statistics with smooth weight functions. The underlying distribution function must possess a finite absolute third moment. This improves an earlier result of the author.

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R. Helmers. "A Berry-Esseen Theorem for Linear Combinations of Order Statistics." Ann. Probab. 9 (2) 342 - 347, April, 1981. https://doi.org/10.1214/aop/1176994478