Wavelets and functional analysis: decomposability and adaptability

• Grant number: 13/01418-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2013
• End date: April 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Parisa Yousefi Zowj
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 14/10827-2 - Statistical models for data that scale: multiscale domain summaries with applications to geophysical data, high frequency biometric responses and medical images, BE.EP.DR

Abstract

The problem of functional estimation has been studied in a myriad of ways. One interesting option is the wavelet functional analysis. Three relevant aspects of this paradigm are: its parsimony, the asymptotic optimality, and its computational performance. The representation of functionals as quasi U-statistics (Pinheiro et al, 2009, 2011) enables one to perform statistical tests for which nice asymptic behavior can be assertained under very mild regularity conditions. The aforementioned methodologies will be applied to original data from genomics, tide levels, and wild animal studies. In case where natural grouping rises it is important to be able to test those differences and pinpoint outstanding individuals in a statistically meaningful way. We propose such an alternative by the quasi U-statistics driven decomposition of non-linear wavelet functional data analysis, and its application to group tests and sparse functional representation. (AU)