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Variable selection and estimation in high‐dimensional models

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  • Joel L. Horowitz

Abstract

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. Sélection des variables et calibration des modèles de grande dimension. Les modèles où les covariables sont de grande dimension émergent fréquemment en économie et dans d'autres champs. Souvent seulement quelques covariables ont un effet significatif sur la variable indépendante. Quand cela se produit, on dit du modèle qu'il est parcimonieux. Dans les applications, cependant, on ne sait pas lesquelles covariables sont importantes et lesquelles ne le sont pas. Ce texte passe en revue des méthodes de discrimination entre variables importantes ou non, en portant une attention particulière aux méthodes qui discriminent correctement avec une probabilité qui s'approche de 1 quand la taille de l'échantillon s'accroît. Des méthodes sont disponibles pour une grande variété de modèles – linéaires, non‐linéaires, semi‐paramétriques et non‐paramétriques. La performance de certaines de ces méthodes pour des échantillons finis est illustrée à l'aide de simulations de Monte Carlo et d'un exemple empirique.

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  • Joel L. Horowitz, 2015. "Variable selection and estimation in high‐dimensional models," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(2), pages 389-407, May.
    • Handle: RePEc:wly:canjec:v:48:y:2015:i:2:p:389-407
    DOI: 10.1111/caje.12130
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    References listed on IDEAS

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    Cited by:

    1. Horowitz, Joel L. & Nesheim, Lars, 2021. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," Journal of Econometrics, Elsevier, vol. 222(1), pages 44-55.
    2. Adriano Zanin Zambom & Gregory J. Matthews, 2021. "Sure independence screening in the presence of missing data," Statistical Papers, Springer, vol. 62(2), pages 817-845, April.

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