PENALIZED MAXIMUM LIKELIHOOD ESTIMATION AND VARIABLE SELECTION IN GEOSTATISTICS

• 成果类型: Article
• 署名作者: Chu, Tingjin; Zhu, Jun; Wang, Haonan
• 署名单位: Colorado State University System; Colorado State University Fort Collins; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS919
• 发表日期: 2011
• 页码: 2607-2625
• 关键词: covariance; regression; shrinkage

摘要

We consider the problem of selecting covariates ill spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and, for ease of computation, PMLE is approximated by one-step sparse estimation (OSE). To further improve computational efficiency, particularly with large sample sizes, we propose penalized maximum covariance-tapered likelihood estimation (PMLET) and its one-step sparse estimation (OSET). General forms of penalty functions with an emphasis on smoothly clipped absolute deviation are used for penalized maximum likelihood. Theoretical properties of PMLE and USE, as well as their approximations PMLET and OSET using covariance tapering, are derived, including consistency, sparsity, asymptotic normality and the oracle properties. For covariance tapering, a by-product of our theoretical results is consistency and asymptotic normality of maximum covariance-tapered likelihood estimates. Finite-sample properties of the proposed methods are demonstrated in a simulation study and, for illustration, the methods are applied to analyze two real data sets.