On guaranteed estimation of the mean of an autoregressive process

V. Konev, S. Pergamenshchikov

    Результат исследования: Материалы для журналаСтатья

    4 Цитирования (Scopus)

    Аннотация

    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.

    Язык оригиналаАнглийский
    Страницы (с... по...)2127-2163
    Количество страниц37
    ЖурналAnnals of Statistics
    Том25
    Номер выпуска5
    Статус публикацииОпубликовано - окт 1997

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    ASJC Scopus subject areas

    • Mathematics(all)
    • Statistics and Probability

    Цитировать

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