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October 2011 Penalized maximum likelihood estimation and variable selection in geostatistics
Tingjin Chu, Jun Zhu, Haonan Wang
Ann. Statist. 39(5): 2607-2625 (October 2011). DOI: 10.1214/11-AOS919


We consider the problem of selecting covariates in 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 OSE, 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.


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Tingjin Chu. Jun Zhu. Haonan Wang. "Penalized maximum likelihood estimation and variable selection in geostatistics." Ann. Statist. 39 (5) 2607 - 2625, October 2011.


Published: October 2011
First available in Project Euclid: 22 December 2011

zbMATH: 1232.86005
MathSciNet: MR2906880
Digital Object Identifier: 10.1214/11-AOS919

Primary: 62F12
Secondary: 62M30

Keywords: covariance tapering , Gaussian process , Model selection , one-step sparse estimation , SCAD , spatial linear model

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 5 • October 2011
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