Significance Testing and Group Variable Selection

TL;DR

This paper introduces an ANOVA-type test for assessing the influence of group variables on a response, and a novel group variable selection method that outperforms existing techniques in various scenarios.

Contribution

It develops a new residual-based ANOVA test and a group variable selection procedure that effectively detects nonlinear effects and heteroscedasticity, outperforming traditional methods like Group Lasso.

Findings

Test outperforms generalized likelihood ratio test in non-additive and heteroscedastic cases.

Selection procedure performs well against Group Lasso, especially for nonlinear effects.

Method demonstrates effectiveness on real data.

Abstract

Let X; Z be r and s-dimensional covariates, respectively, used to model the response variable Y as Y = m(X;Z) + \sigma(X;Z)\epsilon. We develop an ANOVA-type test for the null hypothesis that Z has no influence on the regression function, based on residuals obtained from local polynomial fitting of the null model. Using p-values from this test, a group variable selection method based on multiple testing ideas is proposed. Simulations studies suggest that the proposed test procedure outperforms the generalized likelihood ratio test when the alternative is non-additive or there is heteroscedasticity. Additional simulation studies, with data generated from linear, non-linear and logistic regression, reveal that the proposed group variable selection procedure performs competitively against Group Lasso, and outperforms it in selecting groups having nonlinear effects. The proposed group variable selection procedure is illustrated on a real data set.