A Regularization Approach for Estimation and Variable Selection in High Dimensional Regression

49 Pages Posted: 19 Feb 2019

See all articles by Yiannis Dendramis

Yiannis Dendramis

University of Cyprus - Department of Accounting and Finance

Liudas Giraitis

Queen Mary

George Kapetanios

King's College, London

Date Written: December 27, 2018

Abstract

Model selection and estimation are important topics in econometric analysis which can become considerably complicated in high dimensional settings, where the set of possible regressors can become larger than the set of available observations. For large scale problems the penalized regression methods (e.g. Lasso) have become the de facto benchmark that can effectively trade off parsimony and fit. In this paper we introduce a regularized estimation and model selection approach that is based on sparse large covariance matrix estimation, introduced by Bickel and Levina (2008) and extended by Dendramis, Giraitis, and Kapetanios (2018). We provide asymptotic and small sample results that indicate that our approach can be an important alternative to the penalized regression. Moreover, we also introduce a number of extensions that can improve the asymptotic and small sample performance of the proposed method. The usefulness of what we propose is illustrated via Monte Carlo exercises and an empirical application in macroeconomic forecasting.

Keywords: large dimensional regression, sparse matrix, thresholding, shrinkage, model selection

Suggested Citation

Dendramis, Yiannis and Giraitis, Liudas and Kapetanios, George, A Regularization Approach for Estimation and Variable Selection in High Dimensional Regression (December 27, 2018). Available at SSRN: https://ssrn.com/abstract=3330078 or http://dx.doi.org/10.2139/ssrn.3330078

Yiannis Dendramis (Contact Author)

University of Cyprus - Department of Accounting and Finance ( email )

75 Kallipoleos Street
Nicosia CY 1678, Nicosia P.O. Box 2
Cyprus

Liudas Giraitis

Queen Mary ( email )

Mile End Road
London, London E1 4NS
United Kingdom

HOME PAGE: http://www.econ.qmul.ac.uk/people/liudas-giraitis

George Kapetanios

King's College, London ( email )

30 Aldwych
London, WC2B 4BG
United Kingdom
+44 20 78484951 (Phone)

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