Density deconvolution of different conditional distributions

    Authors

    M. Pensky;A. I. Zayed

    Comments

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    Abbreviated Journal Title

    Ann. Inst. Stat. Math.

    Keywords

    deconvolution; ill-posed problem; probability density; ESTIMATING MIXING DENSITIES; NONPARAMETRIC DECONVOLUTION; MULTIVARIATE; DENSITIES; ASYMPTOTIC NORMALITY; STATIONARY-PROCESSES; INVERSE PROBLEMS; OPTIMAL RATES; WAVELET; DECOMPOSITION; CONVERGENCE; Statistics & Probability

    Abstract

    Recently, a new technique to circumvent the ill-posedness of the deconvolution problem has been suggested. This technique is based on what is known as multi-channel convolution system. In this paper, we modify and develop this technique in order to adapt it for statistical use. We then apply it to the problem of estimation of deconvolution density in the case of different conditional densities. This method enables us to combine equations efficiently for any set of conditional densities and to construct estimators in cases where the characteristic functions of the conditional distributions vanish at some points, as it happens in the cast of uniform and triangular distributions.

    Journal Title

    Annals of the Institute of Statistical Mathematics

    Volume

    54

    Issue/Number

    3

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    701

    Last Page

    712

    WOS Identifier

    WOS:000178679100019

    ISSN

    0020-3157

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