Cramér type large deviations for trimmed L-statisitics

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Cramér type large deviations for trimmed L-statisitics. / Грибкова, Надежда Викторовна.

в: Probability and Mathematical Statistics, Том 37, № 1, 31.01.2017, стр. 101–118 .

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{67814a6b81c94208bb1338abd8ee97fd,

title = "Cram{\'e}r type large deviations for trimmed L-statisitics",

abstract = "In this paper, we propose a~new approach to the investigation of asymptotic properties of trimmedL-statistics and we apply it to the Cram\'{e}r type large deviation problem.Our results can be compared with ones in Callaert et~al.~(1982) -- the first and, as far as we know,~the single article, where some results on probabilities of large deviationsfor 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 Cram\'{e}r type large deviation results for the trimmed $L$-statistics under quite mild and natural conditions.",

keywords = "Trimmed L-statistics, central limit theorem, large deviations, moderate deviations",

author = "Грибкова, {Надежда Викторовна}",

note = "Gribkova N.V. Cram{\'e}r type large deviations for trimmed L-statistics// Probability and Mathematical Statistics, 2017, Vol. 37, N 1, pp. 101–118 ",

year = "2017",

month = jan,

day = "31",

doi = "10.19195/0208-4147.37.1.4",

language = "English",

volume = "37",

pages = "101–118 ",

journal = "Probability and Mathematical Statistics",

issn = "0208-4147",

publisher = "PWN",

number = "1",

}

RIS

TY - JOUR

T1 - Cramér type large deviations for trimmed L-statisitics

AU - Грибкова, Надежда Викторовна

N1 - Gribkova N.V. Cramér type large deviations for trimmed L-statistics// Probability and Mathematical Statistics, 2017, Vol. 37, N 1, pp. 101–118

PY - 2017/1/31

Y1 - 2017/1/31

N2 - In this paper, we propose a~new approach to the investigation of asymptotic properties of trimmedL-statistics and we apply it to the Cram\'{e}r type large deviation problem.Our results can be compared with ones in Callaert et~al.~(1982) -- the first and, as far as we know,~the single article, where some results on probabilities of large deviationsfor 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 Cram\'{e}r type large deviation results for the trimmed $L$-statistics under quite mild and natural conditions.

AB - In this paper, we propose a~new approach to the investigation of asymptotic properties of trimmedL-statistics and we apply it to the Cram\'{e}r type large deviation problem.Our results can be compared with ones in Callaert et~al.~(1982) -- the first and, as far as we know,~the single article, where some results on probabilities of large deviationsfor 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 Cram\'{e}r type large deviation results for the trimmed $L$-statistics under quite mild and natural conditions.

KW - Trimmed L-statistics

KW - central limit theorem

KW - large deviations

KW - moderate deviations

U2 - 10.19195/0208-4147.37.1.4

DO - 10.19195/0208-4147.37.1.4

M3 - Article

VL - 37

SP - 101

EP - 118

JO - Probability and Mathematical Statistics

JF - Probability and Mathematical Statistics

SN - 0208-4147

IS - 1

ER -

ID: 9216091

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