Abstract
U-statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U-statistics make generalizations the empirical mean of a random variable X to the sum of all k-tuples of X observations. This paper examines a setting for nonparametric statistical curve estimation based on an infinite-dimensional covariate, including Stute’s estimator as a special case. In this functional context, the class of “delta sequence estimators” is defined and discussed. The orthogonal series method and the histogram method are both included in this class. We achieve almost complete uniform convergence with the rates of these estimators under certain broad conditions. Moreover, in the same context, we show the uniform almost-complete convergence for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Among the potential applications are discrimination problems, metric learning and the time series prediction from the continuous set of past values.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference126 articles.
1. Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall. Monographs on Statistics and Applied Probability.
2. Nadaraya, E.A. (1989). Nonparametric Estimation of Probability Densities and Regression Curves, Kluwer Academic Publishers Group. Translated from the Russian by Samuel Kotz.
3. Härdle, W. (1990). Applied Nonparametric Regression, Cambridge University Press. Econometric Society Monographs.
4. Wand, M.P., and Jones, M.C. (1995). Kernel Smoothing, Chapman and Hall, Ltd.. Monographs on Statistics and Applied Probability.
5. Eggermont, P.P.B., and LaRiccia, V.N. (2001). Maximum Penalized Likelihood Estimation. Density Estimation. Vol. I, Springer.
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