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

• Grant number: 12/10808-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2012
• End date: March 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Ronaldo Dias
• Grantee: Adriano Zanin Zambom
• Host 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.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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. (12/10808-2)

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. (12/10808-2)

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. (12/22603-6, 12/10808-2)