Analysis of one- and multidimensional time series via quasi $U$-statistics

• Grant number: 07/02767-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2008
• End date: February 28, 2011
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Marcio Valk
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 03/10105-2 - Temporal series, analysis of dependency and applications in actuarial science and finance, AP.PRNX.TEM

Abstract

Pinheiro et al. (2006) shows the decomposability of generalized degenerate $U$-statistics of degree 2 and stationary of order 1 (in Hoeffding's sense). From this decomposibility a martingale process is built based on contrasts of those $U$-statistics. Asymptotic normality is then proved for these quasi $U$-statistics for large sample and/or high dimensions. Sen et al. (2007) generalize the results from Pinheiro et al. (2006) for $U$-statistics of degree $m$ (and also for Von Mises' functionals), and relax some of its regularity conditions. Pinheiro et al. (2005a-c), Pinheiro et al. (2007a-b) use the idea of quasi $U$-statistics and their asymptotic properties for qualitative data in biostatistics. This project aims to adapt the results from Pinheiro et al. (2006) and Sen et al. (2007) uni- and multivariate time series, with direct applications in bioinformatics, ecology, social sciences, inequality indices, and financial time series analysis, with emphasis in the dependence relations. MSC 2000 subject classifications: Primary- 62M10, 62F12; secondary- 60F05.Key words and phrases: Time Series, $U$-statistics, Orthogonal system, Permutation measure, Second-order asymptotics, Second-order decomposability. (AU)

Scientific publications

(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)

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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

VALK, Marcio. The use of quasi U-statistics for univariate and multivariate time series. 2011. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.