Chigansky, Pavel; Klebaner, Fima Compound Poisson approximation for triangular arrays with application to threshold estimation. (English) Zbl 1259.60027 Electron. Commun. Probab. 17, Paper No. 29, 10 p. (2012). Let \(\left\{Y_{n,j},\;j=1,2,\dotsc,n,\;n=1,2,\dots\right\}\) be triangular array of random variables, whose rows are asymptotically negligible and satisfy some weak dependence condition. Using the Tikhomirov method, the authors obtain compound Poisson approximation for the sums \(S_{n}=\sum_{j=1}^{n}Y_{n,j}\). Moreover, they derive bounds on the Levy distance between the distributions function of the sums S\(_{n}\) and the compound Poisson distribution. The results are applied to threshold estimation in autoregressive models. Reviewer: Wiesław Dziubdziela (Kielce) MSC: 60F05 Central limit and other weak theorems 62F12 Asymptotic properties of parametric estimators 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:compound Poisson approximation; weak convergence; Tikhomirov’s method; threshold estimation × Cite Format Result Cite Review PDF Full Text: DOI arXiv