Local minimax pointwise estimation of a multivariate density

E. Belitser

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

    5 Citaten (Scopus)
    1 Downloads (Pure)


    We consider the problem of the nonparametric minimax estimation of a multivariate density at a given point. A concept of smoothness classes in nonparametric minimax estimation problems is proposed. The smoothness of a function is characterized by the approximability of the function at a point by an integral of the product of this function with an approximate identity. We propose a singular integral estimator, an integral of this approximate identity with respect to the empirical distribution function. Under some assumptions on the approximate identity, the bias of the estimator is shown to be of smaller order asymptotically than the variance, and the estimator itself is shown to be asymptotically locally minimax with respect to the quadratic risk in a proper topology.
    Originele taal-2Engels
    Pagina's (van-tot)351-365
    Aantal pagina's15
    TijdschriftStatistica Neerlandica
    Nummer van het tijdschrift3
    StatusGepubliceerd - 2000


    Duik in de onderzoeksthema's van 'Local minimax pointwise estimation of a multivariate density'. Samen vormen ze een unieke vingerafdruk.

    Citeer dit