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

D. Fourdrinier, V. Konev, S. Pergamenshchikov

    Research output: Contribution to journal › Article

    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

    Fingerprint

    Sequential Estimation
    Autoregressive Process
    First-order
    Dependent
    Mixture of Normal Distributions
    Sequential Procedure
    Limiting Distribution
    Unknown Parameters
    Mean Square
    Asymptotic distribution
    Estimator
    Autoregressive process

    Keywords

    • autoregression model
    • truncated sequential estimators
    • uniform normality

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Statistics and Probability

    Cite this

    Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises. / Fourdrinier, D.; Konev, V.; Pergamenshchikov, S.

    In: Mathematical Methods of Statistics, Vol. 18, No. 1, 01.03.2009, p. 43-58.

    Research output: Contribution to journal › Article

    Fourdrinier, D, Konev, V & Pergamenshchikov, S 2009, 'Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises', Mathematical Methods of Statistics, vol. 18, no. 1, pp. 43-58. https://doi.org/10.3103/S1066530709010037
    Fourdrinier D, Konev V, Pergamenshchikov S. Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises. Mathematical Methods of Statistics. 2009 Mar 1;18(1):43-58. https://doi.org/10.3103/S1066530709010037
    Fourdrinier, D. ; Konev, V. ; Pergamenshchikov, S. / Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises. In: Mathematical Methods of Statistics. 2009 ; Vol. 18, No. 1. pp. 43-58.
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