GRID for model structure discovering in high dimensional regression
Francesco Giordano (),
Soumendra Nath Lahiri () and
Maria Lucia Parrella ()
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Francesco Giordano: Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno
Soumendra Nath Lahiri: Statistics Department, NC State University
Maria Lucia Parrella: Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno
No 3_231, Working Papers from Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno
Given a nonparametric regression model, we assume that the number of covariates $d\rightarrow\infty$ but only some of these covariates are relevant for the model. Our goal is to identify the relevant covariates and to obtain some information about the structure of the model. We propose a new nonparametric procedure, called GRID, having the following features: (a) it automatically identifies the relevant covariates of the regression model, also distinguishing the nonlinear from the linear ones (a covariate is defined linear/nonlinear depending on the marginal relation between the response variable and such a covariate); (b) the interactions between the covariates (mixed effect terms) are automatically identified, without the necessity of considering some kind of stepwise selection method. In particular, our procedure can identify the mixed terms of any order (two way, three way, ...) without increasing the computational complexity of the algorithm; (c) it is completely data-driven, so being easily implementable for the analysis of real datasets. In particular, it does not depend on the selection of crucial regularization parameters, nor it requires the estimation of the nuisance parameter $\sigma^2$ (self scaling). The acronym GRID has a twofold meaning: first, it derives from Gradient Relevant Identification Derivatives, meaning that the procedure is based on testing the significance of a partial derivative estimator; second, it refers to a graphical tool which can help in representing the identified structure of the regression model. The properties of the GRID procedure are investigated theoretically.
Keywords: Variable selection; model selection; nonparametric model regression. (search for similar items in EconPapers)
JEL-codes: C14 C15 C18 C88 (search for similar items in EconPapers)
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Published in Working Papers, September 2014, pages 1-26
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