基于协方差近似的ml -协方差参数估计的渐近分析

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY
Reinhard Furrer, Michael Hediger
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引用次数: 0

摘要

给定一个零均值高斯随机场,其协方差函数属于参数协方差函数族,我们引入了似然近似的新概念,称为截断似然函数。截断似然函数基于假定的协方差函数族的直接函数近似。对于紧支持的协方差函数,在渐近框架内,给出了截断似然函数估计量的相合性和渐近正态性保持的充分条件。我们将结果应用于广义温德兰协方差函数族,并讨论了几个温德兰近似的例子。对于不紧支持的协方差函数家族,我们将我们的结果与协方差渐窄方法结合起来,并表明当渐窄范围固定时,基于截断渐窄似然函数的ML估计器可以渐近地最小化Kullback-Leibler散度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions. Truncated-likelihood functions are based on direct functional approximations of the presumed family of covariance functions. For compactly supported covariance functions, within an increasing-domain asymptotic framework, we provide sufficient conditions under which consistency and asymptotic normality of estimators based on truncated-likelihood functions are preserved. We apply our result to the family of generalized Wendland covariance functions and discuss several examples of Wendland approximations. For families of covariance functions that are not compactly supported, we combine our results with the covariance tapering approach and show that ML estimators, based on truncated-tapered likelihood functions, asymptotically minimize the Kullback-Leibler divergence, when the taper range is fixed.
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来源期刊
Electronic Journal of Statistics
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.
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