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Variable selection and estimation in high‐dimensional models
Author(s) -
Horowitz Joel L.
Publication year - 2015
Publication title -
canadian journal of economics/revue canadienne d'économique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 69
eISSN - 1540-5982
pISSN - 0008-4085
DOI - 10.1111/caje.12130
Subject(s) - covariate , econometrics , nonparametric statistics , monte carlo method , model selection , variety (cybernetics) , variable (mathematics) , sample size determination , semiparametric model , semiparametric regression , selection (genetic algorithm) , mathematics , computer science , statistics , machine learning , mathematical analysis
Models with high‐dimensional covariates arise frequently in economics and other fields. Often, only a few covariates have important effects on the dependent variable. When this happens, the model is said to be sparse. In applications, however, it is not known which covariates are important and which are not. This paper reviews methods for discriminating between important and unimportant covariates with particular attention given to methods that discriminate correctly with probability approaching 1 as the sample size increases. Methods are available for a wide variety of linear, nonlinear, semiparametric and nonparametric models. The performance of some of these methods in finite samples is illustrated through Monte Carlo simulations and an empirical example.