高频分数阶高斯噪声的一步估计

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI:10.1051/PS/2020022

A. Brouste, M. Soltane, I. Votsi

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引用次数: 6

摘要

本文研究高频观测方案中分数阶高斯噪声的参数估计问题。研究了Le Cam的一步极大似然估计序列。该序列由基于二次广义变分估计(QGV)的初始序列和单个Fisher评分步骤定义。证明了OSMLE序列作为极大似然估计序列是渐近有效的，但计算量要少得多。相对于方差效率不高的QGV，它也是有利的。通过蒙特卡罗模拟说明了估计器在有限大小观测样本上的性能。

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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One-step estimation for the fractional Gaussian noise at high-frequency

The present paper concerns the parametric estimation for the fractional Gaussian noise in a high-frequency observation scheme. The sequence of Le Cam’s one-step maximum likelihood estimators (OSMLE) is studied. This sequence is defined by an initial sequence of quadratic generalized variations-based estimators (QGV) and a single Fisher scoring step. The sequence of OSMLE is proved to be asymptotically efficient as the sequence of maximum likelihood estimators but is much less computationally demanding. It is also advantageous with respect to the QGV which is not variance efficient. Performances of the estimators on finite size observation samples are illustrated by means of Monte-Carlo simulations.

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.