非规则频谱的海灵格距离估计

IF 0.5 4区 数学 Q4 STATISTICS & PROBABILITY
M. Taniguchi, Y. Xue
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引用次数: 0

摘要

概率论及其应用》(Theory of Probability &Its Applications),第 69 卷第 1 期,第 150-160 页,2024 年 5 月。 对于高斯静止过程,推导出了频谱 $f$ 和 $g$ 的时间序列海灵格距离 $T(f,g)$。计算 $T(f_\theta,f_{\theta+h})$ 的形式为 $O(h^\alpha)$,我们给出了非规则谱的 $\theta$ 最大似然估计值的 1/\alpha$ 一致性渐近。对于规则谱,我们引入了最小海灵格距离估计器 $\widehat{theta}=\operatorname{arg}\min_\theta T(f_\theta,\widehat{g}_n)$ ,其中 $\widehat{g}_n$ 是一个非参数谱密度估计器。我们证明,$\widehat\theta$ 在渐近上是有效的,而且比惠特尔估计器更稳健。我们还提供了简要的数值研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hellinger Distance Estimation for Nonregular Spectra
Theory of Probability &Its Applications, Volume 69, Issue 1, Page 150-160, May 2024.
For Gaussian stationary processes, a time series Hellinger distance $T(f,g)$ for spectra $f$ and $g$ is derived. Evaluating $T(f_\theta,f_{\theta+h})$ of the form $O(h^\alpha)$, we give $1/\alpha$-consistent asymptotics of the maximum likelihood estimator of $\theta$ for nonregular spectra. For regular spectra, we introduce the minimum Hellinger distance estimator $\widehat{\theta}=\operatorname{arg}\min_\theta T(f_\theta,\widehat{g}_n)$, where $\widehat{g}_n$ is a nonparametric spectral density estimator. We show that $\widehat\theta$ is asymptotically efficient and more robust than the Whittle estimator. Brief numerical studies are provided.
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来源期刊
Theory of Probability and its Applications
Theory of Probability and its Applications 数学-统计学与概率论
CiteScore
1.00
自引率
16.70%
发文量
54
审稿时长
6 months
期刊介绍: Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
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