ML85597.pdf (179.12 kB)
Download file

On Hipp's compound Poisson approximations via concentration functions

Download (179.12 kB)
journal contribution
posted on 19.11.2007, 15:45 by P.B. Roos
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.

History

Citation

Bernoulli, 2005, 11 (3), pp.533-557

Version

VoR (Version of Record)

Published in

Bernoulli

Publisher

Bernoulli Society for Mathematical Statistics and Probability and International Statistical Institute (ISI)

issn

1350-7265

Copyright date

2005

Available date

19/11/2007

Publisher version

http://projecteuclid.org/euclid.bj/1120591188

Language

en

Usage metrics

Categories

Keywords

Exports