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Title: On Hipp's compound Poisson approximations via concentration functions
Authors: Roos, P.B.
First Published: 2005
Publisher: Bernoulli Society for Mathematical Statistics and Probability and International Statistical Institute (ISI)
Citation: Bernoulli, 2005, 11 (3), pp.533-557
Abstract: This paper is devoted to a refinement of Hipp's method in the compound Poisson approximation to the distribution of the sum of independent but not necessarily identically distributed random variables. Approximations by related Kornya-Presman signed measures are also considered. By using alternative proofs, we show that several constants in the upper bounds for the Kolmogorov and the stop-loss distances can be reduced. Concentration functions play an important role in Hipp's method. Therefore, we provide an improvement of the constant in Le~Cam's bound for concentration functions of compound Poisson distributions. But we also follow Hipp's idea to estimate such concentration functions with the help of Kesten's concentration function bound for sums of independent random variables. In fact, under the assumption that the summands are identically distributed, we present a smaller constant in Kesten's bound, the proof of which is based on a slight sharpening of Le Cam's version of the Kolmogorov-Rogozin inequality.
DOI Link: 10.3150/bj/1120591188
ISSN: 1350-7265
Version: Publisher version
Status: Peer reviewed
Type: Article
Rights: Copyright © 2005 ISI/BS. Deposited with reference to the publisher's archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Mathematics

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