UNIVERSITY
OF WROC£AW
 
Main Page
Contents of previous volumes
Forthcoming papers
General Information
Instructions for authors


VOLUMES
37.1 36.2 36.1 35.2 35.1 34.2 34.1
33.2 33.1 32.2 32.1 31.2 31.1 30.2
30.1 29.2 29.1 28.2 28.1 27.2 27.1
26.2 26.1 25.2 25.1 24.2 24.1 23.2
23.1 22.2 22.1 21.2 21.1 20.2 20.1
19.2 19.1 18.2 18.1 17.2 17.1 16.2
16.1 15 14.2 14.1 13.2 13.1 12.2
12.1 11.2 11.1 10.2 10.1 9.2 9.1
8 7.2 7.1 6.2 6.1 5.2 5.1
4.2 4.1 3.2 3.1 2.2 2.1 1.2
1.1
 
 
WROC£AW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 37, Fasc. 1,
pages 101 - 118
 

CRAMÉR TYPE LARGE DEVIATIONS FOR TRIMMED L -STATISTICS

Nadezhda Gribkova

Abstract: In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed L -statistics and we apply it to the Cramér type large deviation problem. Our results can be compared with those in Callaert et al. (1982) – the first and, as far as we know, the single article where some results on probabilities of large deviations for the trimmed L -statistics were obtained, but under some strict and unnatural conditions. Our approach is to approximate the trimmed L -statistic by a non-trimmed L -statistic (with smooth weight function) based on Winsorized random variables. Using this method, we establish the Cramér type large deviation results for the trimmed L -statistics under quite mild and natural conditions.

2010 AMS Mathematics Subject Classification: Primary: 62G30, 62E20; Secondary: 60F05, 60F10.

Keywords and phrases: Trimmed L -statistics, central limit theorem, large deviations, moderate deviations.

Download:    Abstract    Full text   Abstract + References