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Algorithm for Hypothesis Testing in Nonparametric Regression and its Asymptotic Properties with Applications to Variable Selection

Grant number: 12/10808-2
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): August 01, 2012
Effective date (End): March 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Statistics
Principal researcher:Ronaldo Dias
Grantee:Adriano Zanin Zambom
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Let X be a d dimensional vector of covariates and Y be the response variable. Underthe nonparametric model Y = m(X) + s(X), the goal is to test if a specic covariate,say Xj ; j=1,...d is signicant in the model. The methodology for completelynonparametric tests has been deeply explored. Zambom and Akritas (2012) proposeda test based on methods of one-way ANOVA when the number of factor levels goes toinnity. One of the objectives of this project is to develop a fast and easy to use software,with many functionalities and controllability over the parameters for the user, providingthe scientic community with the hypothesis test proposed. Using the results of this testZambom e Akritas suggested a variable selection algorithm using FDR (False DiscoveryControl). The algorithm has good results in simulations, but it's asymptotic properties areyet to be explored. Therefore, another objective of this project is to study the theoreticalasymptotic consistency of this algorithm. Other objectives include the study of categoricalpredictors in this analysis, comparison of models with dierent parameters, and others.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
ZAMBOM, ADRIANO ZANIN; AKRITAS, MICHAEL G. Hypothesis testing sure independence screening for nonparametric regression. ELECTRONIC JOURNAL OF STATISTICS, v. 12, n. 1, p. 767-792, 2018. Web of Science Citations: 0.
ZAMBOM, ADRIANO ZANIN; AKRITAS, MICHAEL G. NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection. JOURNAL OF STATISTICAL SOFTWARE, v. 77, n. 10, p. 1-28, APR 2017. Web of Science Citations: 1.
ZAMBOM, ADRIANO ZANIN; AKRITAS, MICHAEL G. NONPARAMETRIC LACK-OF-FIT TESTING AND CONSISTENT VARIABLE SELECTION. STATISTICA SINICA, v. 24, n. 4, p. 1837-1858, OCT 2014. Web of Science Citations: 9.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.