TY - JOUR
T1 - Nonparametric significance testing and group variable selection
AU - Zambom, Adriano Zanin
AU - Akritas, Michael G.
N1 - Funding Information:
The first author was supported by CAPES /Fulbright grant 15087657 and Faepex 573/13 . The second author was supported by National Science Foundation grant DMS-0805598 .
Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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 p-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.
AB - 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 p-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.
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U2 - 10.1016/j.jmva.2014.08.014
DO - 10.1016/j.jmva.2014.08.014
M3 - Article
AN - SCOPUS:84907970195
SN - 0047-259X
VL - 133
SP - 51
EP - 60
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -