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


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)

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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)
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. Web of Science Citations: 2.
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. Web of Science Citations: 3.
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. Web of Science Citations: 0.
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. Web of Science Citations: 1.

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