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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

NONPARAMETRIC LACK-OF-FIT TESTING AND CONSISTENT VARIABLE SELECTION

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Author(s):
Zambom, Adriano Zanin [1] ; Akritas, Michael G. [2]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas, Dept Stat, BR-13083859 Campinas, SP - Brazil
[2] Penn State Univ, Dept Stat, University Pk, PA 16802 - USA
Total Affiliations: 2
Document type: Journal article
Source: STATISTICA SINICA; v. 24, n. 4, p. 1837-1858, OCT 2014.
Web of Science Citations: 9
Abstract

Let X be a d-dimensional vector of covariates and Y be the response variable. Under the nonparametric model Y = m(X) + sigma(X)epsilon we develop an ANOVA-type test for the null hypothesis that a particular coordinate of (X) over dot has no influence on the regression function. The asymptotic distribution of the test statistic, using residuals based on local polynomial regression, is established under the null hypothesis and local alternatives. Simulations suggest that the test outperforms existing procedures in heteroscedastic settings. Using p-values from this test, a variable selection method based on False Discovery Rate corrections is proposed, and proved to be consistent in estimating the set of indices corresponding to the significant covariates. Simulations suggest that, under a sparse model, dimension reduction techniques can help avoid the curse of dimensionality. We also propose a backward elimination version of this procedure, called BEAMS (Backward Elimination ANOVA-type Model Selection), which performs competitively against well-established procedures in linear regression settings, and outperforms them in nonparametric settings. A data set is analyzed. (AU)

FAPESP's process: 12/22603-6 - Hypothesis tests in fixed and mixed effects models and their applications on predictors in ANCOVA and nonparametric regression
Grantee:Ronaldo Dias
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 12/10808-2 - Algorithm for Hypothesis Testing in Nonparametric Regression and its Asymptotic Properties with Applications to Variable Selection
Grantee:Adriano Zanin Zambom
Support type: Scholarships in Brazil - Post-Doctorate