On asymptotic correlation coefficient for some order statistics

Jinliang Wang; Fang Wang; Songbo Hu; Jinliang Wang; Fang Wang; Songbo Hu

doi:10.3934/math.2023344

AIMS Mathematics

2023, Volume 8, Issue 3: 6763-6776. doi: 10.3934/math.2023344

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Research article

On asymptotic correlation coefficient for some order statistics

1.
Science Department of Jiujiang University, Jiangxi Province, China
2.
Jiangxi Province Key Laboratory of Preventive Medicine, School of Public Health, Nanchang University, China

Received: 21 August 2022 Revised: 07 December 2022 Accepted: 14 December 2022 Published: 09 January 2023
MSC : 62F10, 62G30

By the relationship between a continuous population $ X $ and the uniform distribution $ U[0, 1] $, we gain for a sample quantile an equivalent expression of its variance and for two different sample quantiles the asymptotic correlation coefficient. As the population of interest can have no expectation, the obtained conclusions are applicable to the location estimating problem of a Cauchy distribution. On that occasion, we finally obtained a quick and effective estimator established by a linear function of some sample quantiles. For similar problems, the presented approach is worthy of reference.
- asymptotic correlation coefficient,
- location estimating problem,
- lower bound of Cramér-Rao inequality,
- moment convergence,
- order statistic
Citation: Jinliang Wang, Fang Wang, Songbo Hu. On asymptotic correlation coefficient for some order statistics[J]. AIMS Mathematics, 2023, 8(3): 6763-6776. doi: 10.3934/math.2023344

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Abstract

By the relationship between a continuous population $ X $ and the uniform distribution $ U[0, 1] $, we gain for a sample quantile an equivalent expression of its variance and for two different sample quantiles the asymptotic correlation coefficient. As the population of interest can have no expectation, the obtained conclusions are applicable to the location estimating problem of a Cauchy distribution. On that occasion, we finally obtained a quick and effective estimator established by a linear function of some sample quantiles. For similar problems, the presented approach is worthy of reference.

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