NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection

We describe the R package NonpModelCheck for hypothesis testing and variable selection in nonparametric regression. This package implements functions to perform hypothesis testing for the significance of a predictor or a group of predictors in a fully nonparametric heteroscedastic regression model using high-dimensional one-way ANOVA. Based on the p values from the test of each covariate, three different algorithms allow the user to perform variable selection using false discovery rate corrections. A function for classical local polynomial regression is implemented for the multivariate context, where the degree of the polynomial can be as large as needed and bandwidth selection strategies are built in

Sure Independence Screening in the Presence of Data That is Missing at Random

Variable selection in ultra-high dimensional data sets is an increasingly prevalent issue with the readily available data arising from, for example, genome-wide associations studies or gene expression data. When the dimension of the feature space is exponentially larger than the sample size, it is desirable to screen out unimportant predictors in order to bring the dimension down to a moderate scale. In this paper we consider the case when observations of the predictors are missing at random. We propose performing screening using the marginal linear correlation coefficient between each predictor and the response variable accounting for the missing data using maximum likelihood estimation. This method is shown to have the sure screening property. Moreover, a novel method of screening that uses additional predictors when estimating the correlation coefficient is proposed. Simulations show that simply performing screening using pairwise complete observations is out-performed by both the proposed methods and is not recommended. Finally, the proposed methods are applied to a gene expression study on prostate cancer

Non-parametric curve estimation of an autonomous vehicle trajectory

Orientador: Nancy Lopes GarciaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: O objetivo deste estudo 'e encontrar a melhor trajetória para um veiculo autônomo que tem que se locomover de um ponto A 'a um ponto B na menor distancia possível evitando os possíveis obstáculos fixos entre esses pontos. Além disso, assumimos que existe uma distância segura r para ser mantida entre o veículo e os obstáculos. A locomoção do veículo não 'e fácil, isto 'e, o veículo não pode fazer movimentos abruptos e a trajetória tem que seguir uma curva suave. Obviamente, se não ha obstáculos, a melhor rota é uma linha reta entre A e B. Neste trabalho propomos um método não paramétrico de encontrar o melhor caminho. Se ha erro de medida, um estimador estocástico consistente 'e proposto no sentido de que quando o numero de observações aumenta, a trajetória estocástica converge para a determinísticaAbstract: The objective of this study is to find a smooth function joining two points A and B with minimum length constrained to avoid fixed subsets. A penalized nonparametric method of finding the best path is proposed. The method is generalized to the situation where stochastic measurement errors are present. In this case, the proposed estimator is consistent, in the sense that as the number of observations increases the stochastic trajectory converges to the deterministic one. Two applications are immediate, searching the optimal path for an autonomous vehicle while avoiding all fixed obstacles between two points and flight planning to avoid threat or turbulence zonesMestradoMestre em Estatístic