Estimation of a regression with the pulse type noise from discrete data

V. V. Konev, E. A. Pchelintsev, S. M. Pergamenshchikov

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    This paper considers the problem of estimating parameters in a periodic regression in continuous time with a semimartingale noise by discrete time observations. Improved estimates for the regression parameters are proposed. It is established that under some general conditions these estimates have an advantage in the mean square accuracy over the least squares estimates. The asymptotic minimaxity of the improved estimates has been proved in the robust risk sense. The properties of the proposed procedure for the models with non-Gaussian noises of pulse type have been studied. The pulse disturbances have random intensity and occur at random times which form a Poisson process.

    Original languageEnglish
    Pages (from-to)442-457
    Number of pages16
    JournalTheory of Probability and its Applications
    Volume58
    Issue number3
    DOIs
    Publication statusPublished - 2014

    Keywords

    • Asymptotic minimaxity
    • Discrete data
    • Improved estimates
    • Mean square accuracy
    • Pulse type noises
    • Regression model
    • Semimartingale

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

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