GRID for model structure discovering in high dimensional regression

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Abstract
Given a nonparametric regression model, we assume that the number of
covariates d → ∞ 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
datadriven, 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 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.
Collections
Data
2014Autore
Giordano, Francesco
Lahiri, Soumendra Nath
Parrella, Maria Lucia
Metadata
Mostra tutti i dati dell'itemAutori  Giordano, Francesco  
Autori  Lahiri, Soumendra Nath  
Autori  Parrella, Maria Lucia  
Data Realizzazione  20160714T09:46:19Z  
Date Disponibilità  20160714T09:46:19Z  
Data di Pubblicazione  2014  
Identificatore (Citazione)  Giordano, F., Lahiri, S. N. and Parrella, M. L. (2014). “GRID for model structure discovering in high dimensional regression”. DISES Working Paper 3.231, Università degli Studi di Salerno, Dipartimento di Scienze Economiche e Statistiche.  it_IT 
ISSN  19713029  it_IT 
Identificatore (URI)  http://hdl.handle.net/10556/2127  
Abstract  Given a nonparametric regression model, we assume that the number of covariates d → ∞ 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 datadriven, 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 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.  it_IT 
Descrizione fisica  26 p.  it_IT 
Lingua  en  it_IT 
Collezione Digitale  Working Papers ; 3.231  it_IT 
Fonte  UniSa. Sistema Bibliotecario di Ateneo  it_IT 
Soggetto  Variable selection  it_IT 
Soggetto  Model selection  it_IT 
Soggetto  Nonparametric model regression  it_IT 
Titolo  GRID for model structure discovering in high dimensional regression  it_IT 
Tipo  Working Paper  it_IT 