| Full text | |
| Author(s): |
Total Authors: 2
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| 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
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| 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 Opportunities: | 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 Opportunities: | Scholarships in Brazil - Post-Doctoral |