Sankhya: The Indian Journal of Statistics
1996, Volume 58, Series A, Pt. 1, pp. 126--134
AN Lp NONUNIFORM CENTRAL LIMIT BOUND FOR LINEAR COMBINATIONS OF ORDER STATISTICS
TIEE-JIAN WU, University of Houston and Academia Sinica
SUMMARY. Under the assumption that the absolute third moment of the underlying distribution is finite, the ideal Lp, $1 \leq p \leq \infty$, nonuniform (with multiplying factor (1 + |x|)3-1/p) central limit bound of order O(N-1/2) is established for linear combinations of order statistics with weight functions being Lipschitz of order 1 on (0,1). This extends and refines Theorems 3.1.1-3.1.2 of Helmers (1984).
AMS (1980) subject classification. Primary 62G30, 60F05, secondary 62E20.
Key words and phrases. $L_p$ nonuniform central limit bounds, Linear combinations of order statistics.
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