On the Berry-Esseen Bound for $L$-Statistics in the Non-I.D. Case with Applications to the Estimation of Location Parameters
The Annals of Statistics · 1994 · Volume 22 · Issue 2
Abstract
In this paper, two versions of the Berry-Esseen theorems are established for $L$-statistics in the non-identically distributed case. One theorem, which requires $E|X_i|^3 < \infty$, is an extension of the classical Berry-Esseen theorem. Another, proved under the condition $E|X_i|^\alpha < \infty$ for some $\alpha \in (0, 1\rbrack$, seems to be of more interest for statistical inference. Some applications are also discussed.
Keywords
$L$-statistics; 60F05; 62F12; 62G30; Berry-Esseen bound; estimation of location parameter from non-i.d. sample;
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