Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises

Abstract

For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz's distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.

Original language	English
Pages (from-to)	43-58
Number of pages	16
Journal	Mathematical Methods of Statistics
Volume	18
Issue number	1
DOIs	https://doi.org/10.3103/S1066530709010037
Publication status	Published - 1 Mar 2009

Keywords

autoregression model
truncated sequential estimators
uniform normality

ASJC Scopus subject areas

Statistics, Probability and Uncertainty
Statistics and Probability

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abstract = "For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz's distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.",

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author = "D. Fourdrinier and V. Konev and S. Pergamenshchikov",

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