On guaranteed estimation of the mean of an autoregressive process

V. Konev, S. Pergamenshchikov

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    This paper considers the problem of sequential point estimation of the mean of a stable autoregressive process with unknown scale and autoregressive parameters. The construction of a sequential procedure makes use of special stopping rules and some modifications of least-squares estimates. The procedure enables estimating the mean with prescribed mean-square accuracy uniformly in nuisance parameters. The uniform asymptotic normality and the asymptotic minimaxity of the sequential estimate are established. The asymptotic formula for the mean sample size is obtained.

    Original languageEnglish
    Pages (from-to)2127-2163
    Number of pages37
    JournalAnnals of Statistics
    Volume25
    Issue number5
    Publication statusPublished - Oct 1997

    Fingerprint

    Autoregressive Process
    Minimaxity
    Sequential Estimation
    Uniform Asymptotics
    Sequential Procedure
    Point Estimation
    Least Squares Estimate
    Stopping Rule
    Stable Process
    Nuisance Parameter
    Asymptotic Normality
    Asymptotic Formula
    Mean Square
    Sample Size
    Unknown
    Estimate
    Autoregressive process

    Keywords

    • Autoregression
    • Fixed-precision estimators
    • Nuisance parameters
    • Sequential estimation

    ASJC Scopus subject areas

    • Mathematics(all)
    • Statistics and Probability

    Cite this

    Konev, V., & Pergamenshchikov, S. (1997). On guaranteed estimation of the mean of an autoregressive process. Annals of Statistics, 25(5), 2127-2163.

    On guaranteed estimation of the mean of an autoregressive process. / Konev, V.; Pergamenshchikov, S.

    In: Annals of Statistics, Vol. 25, No. 5, 10.1997, p. 2127-2163.

    Research output: Contribution to journalArticle

    Konev, V & Pergamenshchikov, S 1997, 'On guaranteed estimation of the mean of an autoregressive process', Annals of Statistics, vol. 25, no. 5, pp. 2127-2163.
    Konev V, Pergamenshchikov S. On guaranteed estimation of the mean of an autoregressive process. Annals of Statistics. 1997 Oct;25(5):2127-2163.
    Konev, V. ; Pergamenshchikov, S. / On guaranteed estimation of the mean of an autoregressive process. In: Annals of Statistics. 1997 ; Vol. 25, No. 5. pp. 2127-2163.
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