Statistical modeling via wavelets

• Grant number: 20/00646-1
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2020
• End date: August 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Michel Helcias Montoril
• Grantee: Michel Helcias Montoril
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Aluísio de Souza Pinheiro ; Rafael Izbicki

Abstract

One of the main interests in Statistics is the satisfactory modeling of data sets in several different situations and contexts. Due to the computational advances in last years, the use of non-parametric approaches have gained more and more attention of researchers, specially because of the ability of these methods in proposing and/or validating other existing approaches. Besides, it is important to mention the flexibility of non-parametric models, where they are capable of adapting to specific features of the data. A non-parametric tool that has gained importance are wavelet bases. The main reason is their ability of estimating functions with good quality, where they can capture irregularities of functions better than other methods, such as Fourier series. In this project we intend to model data sets using wavelet bases. The main goal is the proposal of new methodologies to estimate discriminant functions for high dimensional data, such as functional data, and the estimation of probability density functions of size-biased data. (AU)