Consistent variable selection for functional regression models

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• 作者：Julian A.A. Collazos^a ; Ronaldo Dias^a ; Adriano Z. Zambom^b ; ^{adriano.zambom@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62G08 ; 62G10 ; 62G20
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：146
• 期：Complete
• 页码：63-71
• 全文大小：1237 K

文摘

The dual problem of testing the predictive significance of a particular covariate, and identification of the set of relevant covariates is common in applied research and methodological investigations. To study this problem in the context of functional linear regression models with predictor variables observed over a grid and a scalar response, we consider basis expansions of the functional covariates and apply the likelihood ratio test. Based on 62e1513" title="Click to view the MathML source">p$p$-values from testing each predictor, we propose a new variable selection method, which is consistent in selecting the relevant predictors from set of available predictors that is allowed to grow with the sample size e10" title="Click to view the MathML source">n$n$. Numerical simulations suggest that the proposed variable selection procedure outperforms existing methods found in the literature. A real dataset from weather stations in Japan is analyzed.