Compound Poisson approximation for triangular arrays with application to threshold estimation

TL;DR

This paper proves the weak convergence of triangular arrays to a compound Poisson distribution and applies this result to estimate threshold parameters in autoregressive models.

Contribution

It introduces a novel proof of weak convergence for triangular arrays to the compound Poisson limit using Tikhomirov's method and applies it to statistical threshold estimation.

Findings

Established weak convergence of triangular arrays to compound Poisson distribution

Applied the theoretical result to autoregressive model threshold estimation

Provided a new methodological approach for statistical convergence proofs

Abstract

We prove weak convergence of 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.