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

Grant number: 07/02767-6
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): May 01, 2008
Effective date (End): 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)

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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, . (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.

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