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

1 Scopus citations

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
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",

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volume = "17",

journal = "Electronic Communications in Probability",

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AU - Chigansky, Pavel

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.

KW - Compound Poisson

KW - Threshold estimation

KW - Tikhomirov's method

KW - Weak convergence

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SN - 1083-589X

VL - 17

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

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Compound Poisson approximation for triangular arrays with application to threshold estimation

Abstract

Keywords

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