Quasi U-statistics, wavelets and decomposability: asymptotics and applications

• Grant number: 09/14176-8
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2009
• End date: October 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Aluísio de Souza Pinheiro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The paradigm of data variation decomposability underlies the statistical theory. Its intuitiveness has generated several methodologies which are easily interpreted as simple ANOVAs. The growing complexification of information has posed a new challenge to statistical analysis in the form of the so-called functional data and the high-dimensional categorical data sets. Functional data allows for the (even if partial) definition of variability and its decomposition (Abramovih et al., 2004; Abramovich and Angelini, 2006). For multi- or infinite-dimensional categorical data variability- and dispersion-based measures are physically irrelevant and spurious. For these categorical problems one should use dissimilarity measures which can be decomposed in an analogous manner to the classical ANOVAs (Pinheiro et al., 2005; 2009). The aim of this project is to theoretically extend the available results in subgroup decomposability fTr quasi U-statistics and wavelet ANOVA functional data models (AU)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PINHEIRO, ALUISIO; SEN, PRANAB KUMAR; PINHEIRO, HILDETE P.. A class of asymptotically normal degenerate quasi U-statistics. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, v. 63, n. 6, p. 1165-1182, DEC 2011. (09/14176-8, 08/51097-6, 08/09286-6)

PINHEIRO, HILDETE P.; KIIHL, SAMARA F.; PINHEIRO, ALUISIO; DOS REIS, SERGIO F.. Asymptotic behavior of the scaled mutation rate estimators. BIOMETRICAL JOURNAL, v. 52, n. 3, p. 400-416, JUN 2010. (09/14176-8, 08/51097-6)

VALK, MARCIO; PINHEIRO, ALUISIO. Time-series clustering via quasi U-statistics. JOURNAL OF TIME SERIES ANALYSIS, v. 33, n. 4, p. 608-619, JUL 2012. (09/14176-8, 08/51097-6, 07/02767-6)

BORDIN, TATIANA B.; PINHEIRO, HILDETE P.; PINHEIRO, ALUISIO. Homogeneity tests among groups for microsatellite data. Journal of Applied Statistics, v. 38, n. 9, p. 1951-1962, 2011. (09/14176-8)