General model selection estimation of a periodic regression with a Gaussian noise

Victor Konev, Serguei Pergamenchtchikov

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary Gaussian noise having unknown correlation function. A general model selection procedure on the basis of arbitrary projective estimates, which does not need the knowledge of the noise correlation function, is proposed. A non-asymptotic upper bound for ℒ2-risk (oracle inequality) has been derived under mild conditions on the noise. For the Ornstein-Uhlenbeck noise the risk upper bound is shown to be uniform in the nuisance parameter. In the case of Gaussian white noise the constructed procedure has some advantages as compared with the procedure based on the least squares estimates (LSE). The asymptotic minimaxity of the estimates has been proved. The proposed model selection scheme is extended also to the estimation problem based on the discrete data applicably to the situation when high frequency sampling can not be provided.

    Original languageEnglish
    Pages (from-to)1083-1111
    Number of pages29
    JournalAnnals of the Institute of Statistical Mathematics
    Volume62
    Issue number6
    DOIs
    Publication statusPublished - Dec 2010

    Keywords

    • Improved estimation
    • Model selection procedure
    • Non-parametric regression
    • Oracle inequality
    • Periodic regression

    ASJC Scopus subject areas

    • Statistics and Probability

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