高阶图灵估计渐近正态性的充分必要条件

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY Bernoulli Pub Date : 2023-11-01 DOI:10.3150/23-bej1587

Jie Chang, Michael Grabchak

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引用次数: 0

摘要

本文建立了高阶图灵估计渐近正态性的充分必要条件。进一步给出了几个易于验证的充分条件。然后使用这些条件来证明这些假设适用于尾部有规则变化的大类别分布。这包括以前没有验证过的渐近正态性的类。

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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Necessary and sufficient conditions for the asymptotic normality of higher order Turing estimators

This paper establishes necessary and sufficient conditions for the asymptotic normality of higher order Turing estimators. It further gives several easy to verify sufficient conditions. These conditions are then used to show that the assumptions hold for large classes of distributions with regularly varying tails. This includes classes for which asymptotic normality had not been previously verified.

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.