Comparison and equality of generalized \(\psi \)-estimators

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Annals of the Institute of Statistical Mathematics Pub Date : 2024-12-04 DOI:10.1007/s10463-024-00916-7

Mátyás Barczy, Zsolt Páles

引用次数: 0

Abstract

We solve the comparison problem for generalized \(\psi \)-estimators introduced by Barczy and Páles (arXiv: 2211.06026, 2022). Namely, we derive several necessary and sufficient conditions under which a generalized \(\psi \)-estimator less than or equal to another \(\psi \)-estimator for any sample. We also solve the corresponding equality problem for generalized \(\psi \)-estimators. We also apply our results for some known statistical estimators such as for empirical expectiles and Mathieu-type estimators and for solutions of likelihood equations in case of normal, a Beta-type, Gamma, Lomax (Pareto type II), lognormal and Laplace distributions.

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广义\(\psi \) -估计量的比较与等价

我们解决了Barczy和Páles （arXiv: 2211.06026,2022）引入的广义\(\psi \) -估计量的比较问题。也就是说，我们得到了对任何样本广义\(\psi \) -估计量小于或等于另一个\(\psi \) -估计量的几个充分必要条件。我们还解决了相应的广义\(\psi \) -估计量的等式问题。我们还将我们的结果应用于一些已知的统计估计量，如经验预期量和mathieu型估计量，以及正态、β型、Gamma、Lomax （Pareto II型）、对数正态和拉普拉斯分布情况下的似然方程的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of the Institute of Statistical Mathematics 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.