Author : Robert Lee Taylor
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (227 download)
Book Synopsis Convergence of Weighted Sums of Random Elements in Type P Space by : Robert Lee Taylor
Download or read book Convergence of Weighted Sums of Random Elements in Type P Space written by Robert Lee Taylor and published by . This book was released on 1979 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of probability density estimation led to estimates in the form of averages or weighted sums of random variables whose values are in function spaces (Parzen (1962) and Rosenblatt (1971)). As a application of the law of the iterated logarithm in linear measurable spaces, Kuelbs (1978) considered the rates of convergence in these density estimates. The estimates are not always averages of sequences of random elements in a Banach space but are more often weighted sums of arrays of random elements where the weights are not necessarily Toeplitz matrices. In this paper the convergence of weighted sums of arrays of random elements in Banach spaces of type p is obtained both in probability and almost surely. As corollaries these results have forms of Pruitt's (1963) and Rohatgi's (1971) results for Banach spaces and also have extensions for the results of Padgett and Taylor (1976). However, exact statements of the theorems are related to the possible applications for density estimation.
