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

D. Fourdrinier, V. Konev, S. Pergamenshchikov

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    6 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)43-58
    Number of pages16
    JournalMathematical Methods of Statistics
    Volume18
    Issue number1
    DOIs
    Publication statusPublished - 1 Mar 2009

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    Keywords

    • autoregression model
    • truncated sequential estimators
    • uniform normality

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Statistics and Probability

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