Fixed-domain asymptotics for a subclass of Matern-type Gaussian random fields

• 成果类型: Article
• 署名作者: Loh, WL
• 署名单位: National University of Singapore; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000516
• 发表日期: 2005
• 页码: 2344-2394
• 关键词: maximum-likelihood-estimation; parameters

摘要

Stein [Statist. Sci. 4 (1989) 432-433] proposed the Matern-type Gaussian random fields as a very flexible class of models for computer experiments. This article considers a subclass of these models that are exactly once mean square differentiable. In particular, the likelihood function is determined in closed form, and under mild conditions the sieve maximum likelihood estimators for the parameters of the covariance function are shown to be weakly consistent with respect to fixed-domain asymptotics.