A SELF-NORMALIZED LIL FOR CONDITIONALLY TRIMMED SUMS AND CONDITIONALLY CENSORED SUMS

- Journal title : Journal of the Korean Mathematical Society
- Volume 43, Issue 4, 2006, pp.859-869
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2006.43.4.859

Title & Authors

A SELF-NORMALIZED LIL FOR CONDITIONALLY TRIMMED SUMS AND CONDITIONALLY CENSORED SUMS

Pang Tian Xiao; Lin Zheng Yan;

Pang Tian Xiao; Lin Zheng Yan;

Abstract

Let {} be a sequence of random variables which belong to the attraction of the normal law, and be an arrangement of in decreasing order of magnitude, i.e., . Suppose that {} is a sequence of constants satisfying some mild conditions and d'() is an appropriate truncation level, where is any constant larger than one. Then we show that the conditionally trimmed sums obeys the self-normalized law of the iterated logarithm (LIL). Moreover, the self-normalized LIL for conditionally censored sums is also discussed.

Keywords

self-normalized;law of the iterated logarithm;trimmed sums;censored sums; random variables;

Language

English

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