Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T18:34:48.300Z Has data issue: false hasContentIssue false

The Berry-Esseen bound for the Poisson shot-noise

Published online by Cambridge University Press:  01 July 2016

John A. Lane*
Affiliation:
University College of Wales, Aberystwyth
*
Postal address: Department of Mathematics, The University College of Wales, Aberystwyth, SY23 3BZ, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note provides a useful extension of the Berry–Esseen bound on the error in the normal approximation for shot-noise. The special cases treated are of particular interest in the statistical analysis of Poisson processes and cluster point processes.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1987 

References

Heinrich, L. and Schmidt, V. (1985) Normal convergence of multidimensional shot-noise and rates of this convergence. Adv. Appl. Prob. 17, 709730.Google Scholar
Krickeberg, K. (1982) Processus Ponctuels en Statistique. Lecture Notes in Mathematics 929, 206313. Springer-Verlag, Berlin.Google Scholar
Lane, J. A. (1979) Some Limit Theorems for Shot-noise Processes. Unpublished Ph.D. Thesis, University of London.Google Scholar
Lane, J. A. (1984) The central limit theorem for the Poisson shot-noise process. J. Appl. Prob. 21, 287301.Google Scholar
Neyman, J. and Scott, E. L. (1958) Statistical approach to the problems of cosmology. J.R. Statist. Soc. B 20, 143.Google Scholar
Papoulis, A. (1971) High density shot-noise and gaussianity. J. Appl. Prob. 8, 118127.CrossRefGoogle Scholar
Vere-Jones, D. (1970) Stochastic models for earthquake occurrence. J.R. Statist. Soc. B 32, 162.Google Scholar