Nonparametric significance testing and group variable selection

In the context of a heteroscedastic nonparametric regression model, we develop a test for the null hypothesis that a subset of the predictors has no influence on the regression function. The test uses residuals obtained from local polynomial fitting of the null model and is based on a test statistic inspired from high-dimensional analysis of variance. Using pp-values from this test, and multiple testing ideas, a group variable selection method is proposed, which can consistently select even groups of variables with diminishing predictive significance. A backward elimination version of this procedure, called GBEAMS for Group Backward Elimination Anova-type Model Selection, is recommended for practical applications. Simulation 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 reveal that the proposed group variable selection procedure performs competitively against other variable selection methods, and outperforms them in selecting groups having nonlinear or dependent effects. The proposed group variable selection procedure is illustrated on a real data set.