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Stable Domains of Attraction for Empirical Processes on Vapnik-Červonenkis Classes of Functions

出版	Texas A & M University, 1987
URL	http://books.google.com.hk/books?id=YzP0NwAACAAJ&hl=&source=gbs_api

註釋The main goal of this dissertation is to extend Alexander's (1987) central limit theorem for empirical processes on Vapnik-Cervonenkis classes of functions to the case with non-Gaussian stable Radon limit. The dissertation is divided into four chapters. The first one presents a review on the theory of empirical processes; it also contains the definitions and previous results needed in the following chapters. In the second chapter, we study the entropy of Vapnik-Cervonenkis classes of functions and we prove an exponential inequality similar to one in Alexander (1987). The main results are established in Chapter three. In the first section we give a different proof of Alexander's central limit theorem for empirical processes on Vapnik-Cervonenkis classes of functions. The second section contains sufficient conditions for the process {f(X): f [epsilon] F} to be in the normal domain of attraction of a p-stable Radon measure in l[superscript infinity](F),1 [less than or equal to] p