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

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › 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	American English
Journal	Electronic Communications in Probability
Volume	17
DOIs	https://doi.org/10.1214/ECP.v17-2009
State	Published - 2012

Keywords

Compound Poisson
Threshold estimation
Tikhomirov's method
Weak convergence

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10.1214/ECP.v17-2009

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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.",

keywords = "Compound Poisson, Threshold estimation, Tikhomirov's method, Weak convergence",

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

year = "2012",

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

language = "American English",

volume = "17",

journal = "Electronic Communications in Probability",

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publisher = "Institute of Mathematical Statistics",

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T1 - Compound Poisson approximation for triangular arrays with application to threshold estimation

AU - Chigansky, Pavel

AU - Klebaner, Fima C.

PY - 2012

Y1 - 2012

N2 - 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.

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.

KW - Compound Poisson

KW - Threshold estimation

KW - Tikhomirov's method

KW - Weak convergence

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U2 - 10.1214/ECP.v17-2009

DO - 10.1214/ECP.v17-2009

M3 - Article

AN - SCOPUS:84864721322

SN - 1083-589X

VL - 17

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

Compound Poisson approximation for triangular arrays with application to threshold estimation

Abstract

Keywords

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