SPECIAL SEMINAR: Aluisio Pinheiro, University of Campinas

Topic: Weighted U-Statistics

Abstract: Following the seminal papers of Hoeffding (1948,1961), consider statistics that can be defined as linear combinations of finite-dimensional symmetric functions of the data. These statistics are commonly known as weighted U-statistics. We discuss here some variants, such as : degenerate U-statistics (Dynkin ad Mandelaum, 1983); incomplete U-statistics (Janson, 1984); conditional U-statistics (Stute, 1991); and quasi U-statistics (Pinheiro et al., 2009, 2011, 2014). We study the main issues concerning the weights on each class with main focus on asymptotic behavior, specially under the important case of degeneracy of test statistics under the null hypothesis. We show that quasi U-statistics can be useful for high-dimensional data and dissimilarity measures apportionment. We present some applications to genetics, education, time series analysis and neurosciences.