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July, 1989 Asymptotic Normality and Subsequential Limits of Trimmed Sums
Philip S. Griffin, William E. Pruitt
Ann. Probab. 17(3): 1186-1219 (July, 1989). DOI: 10.1214/aop/1176991264


Let $\{X_i\}$ be i.i.d. and $S_n(s_n, r_n)$ the sum of the first $n X_i$ with the $r_n$ largest and $s_n$ smallest excluded. Assume $r_n \rightarrow \infty, s_n \rightarrow \infty, n^{-1}r_n \rightarrow 0, n^{-1}s_n \rightarrow 0.$ Necessary and sufficient conditions are obtained for the existence of $\{\delta_n\}, \{\gamma_n\}$ such that $\gamma^{-1}_n(S_n(s_n, r_n) - \delta_n)$ converges weakly to a standard normal. The set of all subsequential limit laws for these sequences is characterized and sufficient conditions are given for $X_i$ to be in the domain of partial attraction of a given law in the class. These conditions are also necessary if a unique factorization result for characteristic functions is true.


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Philip S. Griffin. William E. Pruitt. "Asymptotic Normality and Subsequential Limits of Trimmed Sums." Ann. Probab. 17 (3) 1186 - 1219, July, 1989.


Published: July, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0688.60016
MathSciNet: MR1009452
Digital Object Identifier: 10.1214/aop/1176991264

Primary: 60F05

Keywords: asymptotic normality , discarding outliers , stochastic compactness

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 3 • July, 1989
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