Wavelets, quasi U-statistics and functional estimation: decomposability and adaptability

• Grant number: 21/04468-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2021
• End date: January 09, 2022
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Jaime Enrique Lincovil Curivil
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/04654-9 - Time series, wavelets and high dimensional data, AP.TEM

Abstract

Functional data pose two roadblocks to standard statistical methodologies: the complexities intra-observation and the impossibility of employing computacionally inefficient procedures. Relevant numerical and statistical questions include: spurious correlations; escalability; false discovery ratios repetibility; ad reprodutibility (Fan et al, 2000; Johnstone, and Titterington, 2009; Morettin et al., 2017). We propose the representation of each functional by quasi U-statistics. This enables us to develop tests which have solid asymptotic properties (Pinheiro et al, 2009, 2011). The proposed procedures will be applied to genomics, images, among other ultra-high dimensional data. MSC 2000: Primary 62G05; Secondary 62P10. (AU)