Asymptotically minimax nonparametric regression in $L_2$

E.N. Belitser, B.Y. Levit

    Research output: Contribution to journalArticleAcademicpeer-review

    5 Citations (Scopus)

    Abstract

    Additive nonparametric regression with equidistant observation design is considered. The Pinsker-type minimax results are derived and the linear asymptotically minimax estimators are exhibited, based on approximation of the initial nonparametric model by a linear models of dimension which is increasing with the number of observations. The proof of optimality of these linear estimators within the class of all possible estimators is based on the rather elementary but very useful van Trees inequality. Keywords: Ellipsoid; asymptotic minimax risk; Bayes risk; asymptotically minimax estimator; second-order rate minimax estimator.
    Original languageEnglish
    Pages (from-to)105-122
    JournalStatistics
    Volume28
    Issue number2
    DOIs
    Publication statusPublished - 1996

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