Decomposability and asymptotic normality for quasi U-statistics of degree M

• Grant number: 06/04897-1
• Support Opportunities: Scholarships abroad - Research
• Start date: January 25, 2007
• End date: February 24, 2007
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Aluísio de Souza Pinheiro
• Host Investigator: Pranab Kumar Sen
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of North Carolina at Chapel Hill (UNC), United States

Abstract

Pinheiro et al. (2006a) shows the decomposability of generalized U-statistics of degree 2 and stationary of order 1 (in Hoeffding (1948)'s sense). Based on this decomposability property, a martingale array process is built on contrasts of these degenerate U-statistics. It is then shown that these contrasts are asymptotically normal for either large sample sizes and/or high dimensional setups. Pinheiro et al (2006b) generalizes these results for U-statistics of degree m. The visit to Chapel would aim a further generalization concerning the independency assumption that both aforementioned works use. Moreover, these generalizations would be used to study the asymptotic properties of several diversity indices in the literature, with immediate applications in bioinformatics, ecology, social sciences and financial series. (AU)