Boaren: Improving Regularization in Linear Regression With an Application to Index Tracking

Abstract

In this paper we introduce the Arbitrary Rectangle-range Elastic Net (AREN): an elastic net with coefficients restricted to some rectangle in , . The AREN method is one of many regularization techniques intended to increase prediction accuracy in linear regression models by shrinking the magnitude (and possibly eliminating some) of the regression coefficients in an effort to control over-fitting and under-fitting. In this work we describe the AREN features and discuss its statistical consistency properties in estimation and in selecting the correct set of predictors. We also introduce bootstrapping as a way to improve the “small-sample” performance of AREN in selecting predictors. We then apply the AREN (with and without bootstrapping) to tracking the value of the S&P 500 index using a reduced set of stocks.