Inference for Support Vector Regression under ℓ1 Regularization

Abstract

We provide large-sample distribution theory for support vector regression (SVR) with l1-norm along with error bars for the SVR regression coefficients. Although a classical Wald confidence interval obtains from our theory, its implementation inherently depends on the choice of a tuning parameter that scales the variance estimate and thus the width of the error bars. We address this shortcoming by further proposing an alternative large-sample inference method based on the inversion of a novel test statistic that displays competitive power properties and does not depend on the choice of a tuning parameter.