Estatística não-paramétrica: estimação, classificação e uma nova abordagem de seleção automática para largura de banda

Abstract

The thesis initial motivation was to know the state-of-the-art in non-parametric density estimation, compare different situations and assess their impact on the likelihood-based classification. Therefore, a study was carried out related to the automatic choice of bandwidth, the main parameter used by the four classic non-parametric estimators: Histogram, Average Shifted Histogram, Frequency Polygon and Kernel Density Estimation (KDE). In general, the KDE method showed the best results in all tested distributions and, due to this performance, its analysis was further developed, entering into the variable KDE theories with variable bandwidth. Furthermore, several tests shown that the selectors based on cross-validation are more resilient than the Plug-In methods, leading to better density estimation and classification results in complex problems. Finally, this thesis unfolded in some contributions to the state-of-the-art in the investigation subject, whose main ones are listed below: increased knowledge about some of the main non-parametric estimators discussed in the scientific world; development of a technique for evaluating density estimators called the Region of Interest Map (RoIMap); proposal for a hybrid automatic technique to adjust the variable bandwidth selector called Region of interest-based kernel density estimation (ROIKDE); and impact evaluation of the nonparametric estimation in classifying samples.