An Algorithm for Nonlinear, Nonparametric Model Choice and Prediction - INSA Toulouse - Institut National des Sciences Appliquées de Toulouse Accéder directement au contenu
Article Dans Une Revue Journal of Computational and Graphical Statistics Année : 2015

An Algorithm for Nonlinear, Nonparametric Model Choice and Prediction

Résumé

We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, aims to choose those combinations of vector components that provide best prediction. The algorithm is constructed specifically so that it devotes attention to components that might be of relatively little predictive value by themselves, and so might be ignored by more conventional methodology for model choice, but which, in combination with other difficult-to-find components, can be particularly beneficial for prediction. The design of the algorithm is also motivated by a desire to choose vector components that become redundant once appropriate combinations of other, more relevant components are selected. Our theoretical arguments show these goals are met in the sense that, with probability converging to 1 as sample size increases, the algorithm correctly determines a small, fixed number of variables on which the regression mean, g say, depends, even if dimension diverges to infinity much faster than n. Moreover, the estimated regression mean based on those variables approximates g with an error that, to first order, equals the error which would arise if we were told in advance the correct variables. In this sense, the estimator achieves oracle performance. Our numerical work indicates that the algorithm is suitable for very high dimensional problems, where it keeps computational labor in check by using a novel sequential argument, and also for more conventional prediction problems, where dimension is relatively low.
Fichier principal
Vignette du fichier
ferraty-hall-JCGS-preprint (2).pdf (335.75 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01980191 , version 1 (23-01-2019)

Identifiants

Citer

Frédéric Ferraty, Peter Hall. An Algorithm for Nonlinear, Nonparametric Model Choice and Prediction. Journal of Computational and Graphical Statistics, 2015, 24 (3), pp.695-714. ⟨10.1080/10618600.2014.936605⟩. ⟨hal-01980191⟩
39 Consultations
40 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More