Compound Poisson approximation for triangular arrays with application to threshold estimation

Pavel Chigansky; Fima C Klebaner

doi:10.1214/ECP.v17-2009

Compound Poisson approximation for triangular arrays with application to threshold estimation

Pavel Chigansky, Fima C Klebaner

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

We prove weak convergence of sums over triangular arrays to the compound Poisson limit using Tikhomirov s method. The result is applied to statistical estimation of the threshold parameter in autoregressive models.

Original language	English
Pages (from-to)	1 - 10
Number of pages	10
Journal	Electronic Communications in Probability
Volume	17
DOIs	https://doi.org/10.1214/ECP.v17-2009
Publication status	Published - 2012

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10.1214/ECP.v17-2009

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Cite this

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title = "Compound Poisson approximation for triangular arrays with application to threshold estimation",

abstract = "We prove weak convergence of sums over triangular arrays to the compound Poisson limit using Tikhomirov s method. The result is applied to statistical estimation of the threshold parameter in autoregressive models.",

author = "Pavel Chigansky and Klebaner, {Fima C}",

year = "2012",

doi = "10.1214/ECP.v17-2009",

language = "English",

volume = "17",

pages = "1 -- 10",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

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AU - Klebaner, Fima C

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AB - We prove weak convergence of sums over triangular arrays to the compound Poisson limit using Tikhomirov s method. The result is applied to statistical estimation of the threshold parameter in autoregressive models.

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DO - 10.1214/ECP.v17-2009

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EP - 10

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

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