连续噪声数据中Hurst参数的估计

IF 1 4区数学 Q3 STATISTICS & PROBABILITY

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI:10.1214/23-ejs2156

Pavel Chigansky, Marina Kleptsyna

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引用次数: 1

摘要

研究了从连续时间噪声样本中估计分数阶布朗运动的赫斯特指数的问题。当赫斯特参数大于3∕4时，只有当观测区间的长度增大到无穷大或噪声强度减小到零时，才有可能进行一致估计。主要结果是证明了模型在这两种情况下的局部渐近正态性，揭示了最优的极大极小估计率。

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Estimation of the Hurst parameter from continuous noisy data

This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. When the Hurst parameter is greater than 3∕4, consistent estimation is possible only if either the length of the observation interval increases to infinity or intensity of the noise decreases to zero. The main result is a proof of the Local Asymptotic Normality (LAN) of the model in these two regimes which reveals the optimal minimax estimation rates.

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来源期刊

Electronic Journal of Statistics STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

9.10%

发文量

100

审稿时长

3 months

期刊介绍： The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.