一般m估计量的正态逼近在L1 Wasserstein距离上的界

IF 1 4区数学 Q3 STATISTICS & PROBABILITY

Electronic Journal of Statistics Pub Date : 2021-11-18 DOI:10.1214/23-ejs2132

F. Bachoc, M. Fathi

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引用次数: 0

摘要

我们导出了一般M-估计量在$L^1$Wasserstein距离内收敛速度的定量界，在观测次数上具有几乎尖锐的（高达对数项）行为。我们关注的是估计器没有作为数据函数的显式表达式的情况。即使在观测不独立的情况下，也可以应用通用方法。我们的主要应用是高斯过程协方差参数的交叉验证估计的收敛速度。

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Bounds in L1 Wasserstein distance on the normal approximation of general M-estimators

We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the estimator does not have an explicit expression as a function of the data. The general method may be applied even in situations where the observations are not independent. Our main application is a rate of convergence for cross validation estimation of covariance parameters of Gaussian processes.

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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.