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.
News published in Agência FAPESP Newsletter about the scholarship: