On moment convergence of sample quantiles with application to parameter estimations for Cauchy distribution

Yuankang Wang; Yuankang Wang

doi:10.3934/math.20251358

AIMS Mathematics

2025, Volume 10, Issue 12: 30942-30967. doi: 10.3934/math.20251358

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Research article

On moment convergence of sample quantiles with application to parameter estimations for Cauchy distribution

Yuankang Wang ^,

School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China

Received: 08 October 2025 Revised: 14 December 2025 Accepted: 22 December 2025 Published: 31 December 2025
MSC : 62F10

Under a general condition on continuous probability distributions of some populations, this study establishes that the distributional convergence of sample quantiles implies moment convergence. As an application, we propose a quick and robust consistent estimator for the shape parameter of the Cauchy distribution under large-sample conditions. This estimator achieves over 99% efficiency relative to the maximum likelihood estimator.
- asymptotically consistent estimator,
- Cauchy distribution,
- convergence in distribution,
- convergence of moments
Citation: Yuankang Wang. On moment convergence of sample quantiles with application to parameter estimations for Cauchy distribution[J]. AIMS Mathematics, 2025, 10(12): 30942-30967. doi: 10.3934/math.20251358

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Abstract

Under a general condition on continuous probability distributions of some populations, this study establishes that the distributional convergence of sample quantiles implies moment convergence. As an application, we propose a quick and robust consistent estimator for the shape parameter of the Cauchy distribution under large-sample conditions. This estimator achieves over 99% efficiency relative to the maximum likelihood estimator.

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