Variable Selection for High-Dimensional Spatial Regression Models

• Activity Number: 235 - Spatio-Temporal Theory and Methods
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Abolfazl Safikhani* and Tapabrata Maiti and Chae Young Lim
• Companies: Columbia University and Michigan State University and Seoul National University
• Keywords: high dimensional Variable selection ; covariance estimation ; penalized likelihood ; spatial regression

Abstract

We consider a problem for spatial regression where the number of covariates increases with the number of sampling locations and the spatial covariance is unknown up to a finite number of parameters. We propose a penalized likelihood based approach with bridge-type penalization for simultaneous variable selection and covariance parameter estimation. Consistency of the proposed method is derived and the effect of spatial covariance structure on the convergence rate is investigated. Further, by putting appropriate analytical conditions on the spatial covariance formation, the oracle properties and asymptotic normality of the proposed method is developed. Finally, the performance of the selection and estimation procedure is illustrated empirically through various scenarios of covariance functions.