FIXED-DOMAIN ASYMPTOTIC PROPERTIES OF TAPERED MAXIMUM LIKELIHOOD ESTIMATORS

• 成果类型: Article
• 署名作者: Du, Juan; Zhang, Hao; Mandrekar, V. S.
• 署名单位: Michigan State University; Purdue University System; Purdue University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS676
• 发表日期: 2009
• 页码: 3330-3361
• 关键词: linear predictions; random-field; covariance; interpolation; parameters; MODEL

摘要

When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency of the maximum likelihood estimator (MLE) for the microergodic parameter in the Matern covariance function by establishing the fixed-domain asymptotic distribution of the exact MLE and that of the tapered MLE. Our results imply that, under some conditions on the taper, the tapered MLE is asymptotically as efficient as the true MLE for the microergodic parameter in the Matern model.