On optimality of the fixed-accuracy estimate of the parameter in an explosive autoregressive process of the first order

V. V. Konev, S. M. Pergamenshchikov

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    The uniform asymptotic normality of the fixed accuracy estimate for the parameter in explosive autoregressive process of the first order is established. The asymptotic optimality of the estimate in minimax sense for sufficiently broad class of loss functions is shown. The fixed-accuracy estimate is constructed as a sequential modification of the least squares estimate.

    Original languageEnglish
    Pages (from-to)25-78
    Number of pages54
    JournalSequential Analysis
    Volume12
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 1993

    Fingerprint

    Autoregressive Process
    Optimality
    First-order
    Estimate
    Uniform Asymptotics
    Asymptotic Optimality
    Least Squares Estimate
    Loss Function
    Asymptotic Normality
    Minimax

    Keywords

    • asymptotic normality
    • autoregressive process
    • optimality in minimax sense
    • sequential estimate
    • stopping time

    ASJC Scopus subject areas

    • Modelling and Simulation
    • Statistics and Probability

    Cite this

    On optimality of the fixed-accuracy estimate of the parameter in an explosive autoregressive process of the first order. / Konev, V. V.; Pergamenshchikov, S. M.

    In: Sequential Analysis, Vol. 12, No. 1, 01.01.1993, p. 25-78.

    Research output: Contribution to journalArticle

    @article{ba7a0cac26d3466c8f872bb3937154f8,
    title = "On optimality of the fixed-accuracy estimate of the parameter in an explosive autoregressive process of the first order",
    abstract = "The uniform asymptotic normality of the fixed accuracy estimate for the parameter in explosive autoregressive process of the first order is established. The asymptotic optimality of the estimate in minimax sense for sufficiently broad class of loss functions is shown. The fixed-accuracy estimate is constructed as a sequential modification of the least squares estimate.",
    keywords = "asymptotic normality, autoregressive process, optimality in minimax sense, sequential estimate, stopping time",
    author = "Konev, {V. V.} and Pergamenshchikov, {S. M.}",
    year = "1993",
    month = "1",
    day = "1",
    doi = "10.1080/07474949308836269",
    language = "English",
    volume = "12",
    pages = "25--78",
    journal = "Sequential Analysis",
    issn = "0747-4946",
    publisher = "Taylor and Francis Ltd.",
    number = "1",

    }

    TY - JOUR

    T1 - On optimality of the fixed-accuracy estimate of the parameter in an explosive autoregressive process of the first order

    AU - Konev, V. V.

    AU - Pergamenshchikov, S. M.

    PY - 1993/1/1

    Y1 - 1993/1/1

    N2 - The uniform asymptotic normality of the fixed accuracy estimate for the parameter in explosive autoregressive process of the first order is established. The asymptotic optimality of the estimate in minimax sense for sufficiently broad class of loss functions is shown. The fixed-accuracy estimate is constructed as a sequential modification of the least squares estimate.

    AB - The uniform asymptotic normality of the fixed accuracy estimate for the parameter in explosive autoregressive process of the first order is established. The asymptotic optimality of the estimate in minimax sense for sufficiently broad class of loss functions is shown. The fixed-accuracy estimate is constructed as a sequential modification of the least squares estimate.

    KW - asymptotic normality

    KW - autoregressive process

    KW - optimality in minimax sense

    KW - sequential estimate

    KW - stopping time

    UR - http://www.scopus.com/inward/record.url?scp=0040013711&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0040013711&partnerID=8YFLogxK

    U2 - 10.1080/07474949308836269

    DO - 10.1080/07474949308836269

    M3 - Article

    VL - 12

    SP - 25

    EP - 78

    JO - Sequential Analysis

    JF - Sequential Analysis

    SN - 0747-4946

    IS - 1

    ER -