Nonparametric significance testing and group variable selection

Adriano Zanin Zambom, Michael G. Akritas

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)51-60
Number of pages10
JournalJournal of Multivariate Analysis
Volume133
DOIs
StatePublished - Jan 1 2015

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Variable Selection
Testing
Selection Procedures
Analysis of variance (ANOVA)
Elimination
Local Polynomial Fitting
Statistics
Polynomials
Simulation Study
Heteroscedastic Regression
Generalized Likelihood Ratio Test
Heteroscedasticity
Multiple Testing
Diminishing
Dimensional Analysis
Nonparametric Model
Analysis of variance
Nonparametric Regression
Regression Function
p-Value

All Science Journal Classification (ASJC) codes

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

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Nonparametric significance testing and group variable selection. / Zambom, Adriano Zanin; Akritas, Michael G.

In: Journal of Multivariate Analysis, Vol. 133, 01.01.2015, p. 51-60.

Research output: Contribution to journalArticle

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