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Marianna Pensky

  1. Adaptive Nonparametric Empirical Bayes Estimation Via Wavelet Series.

    Mon, 05/07/2012 - 15:01 — SomNambul
    Authors: Marianna Pensky, Rida Benhaddou
    Subjects: Statistics
    Abstract

    The present paper proposes generalization of the linear empirical Bayes
    estimation method which takes advantage of the flexibility of the wavelet
    techniques. We present an empirical Bayes estimator as a wavelet series
    expansion and estimate coefficients by minimizing the prior risk of the
    estimator. As a result, estimation of wavelet coefficients requires solution of
    a well-posed low-dimensional sparse system of linear equations. The dimension
    of the system depends on the size of wavelet support and smoothness of the
    Bayes estimator.

  2. Laplace deconvolution with noisy observations.

    Fri, 07/15/2011 - 15:01 — SomNambul
    Authors: Marianna Pensky, Felix Abramovich, Yves Rozenholc
    Subjects: Statistics
    Abstract

    In the present paper we consider Laplace deconvolution on the basis of
    discrete noisy data observed on the interval which length may increase with a
    sample size. Although this problem arises in a variety of applications, to the
    best of our knowledge, it has not been systematically studied in statistical
    literature and the present paper contributes to fill this gap. We derive an
    adaptive kernel estimator of the function of interest, and establish its
    asymptotic minimaxity over a range of Sobolev classes.

  3. Nonparametric Regression Estimation with Incomplete Data: Minimax Global Convergence Rates and Adaptivity.

    Thu, 06/23/2011 - 15:01 — SomNambul
    Authors: Marianna Pensky, Theofanis Sapatinas, Anestis Antoniadis
    Subjects: Methodology
    Abstract

    We consider the nonparametric regression estimation problem of recovering an
    unknown response function $f$ on the basis of incomplete data when the design
    points follow a known density $g$ with a finite number of well separated zeros.
    In particular, we consider two different cases: when $g$ has zeros of a
    polynomial order and when $g$ has zeros of an exponential order. These two
    cases correspond to moderate and severe data losses, respectively.

  4. Multichannel Boxcar Deconvolution with Growing Number of Channels.

    Mon, 02/14/2011 - 16:01 — SomNambul
    Authors: Marianna Pensky, Theofanis Sapatinas
    Subjects: Statistics
    Abstract

    We consider the problem of estimating the unknown response function in the
    multichannel deconvolution model with a boxcar-like kernel which is of
    particular interest in signal processing. It is known that, when the number of
    channels is finite, the precision of reconstruction of the response function
    increases as the number of channels $M$ grow (even when the total number of
    observations $n$ for all channels $M$ remains constant) and this requires that
    the parameter of the channels form a Badly Approximable $M$-tuple.

  5. On Convergence Rates Equivalency and Sampling Strategies in Functional Deconvolution Models.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Marianna Pensky, Theofanis Sapatinas
    Subjects: gr. Statistics
    Abstract

    Using the asymptotical minimax framework, we examine convergence rates
    equivalency between a continuous functional deconvolution model and its
    real-life discrete counterpart, over a wide range of Besov balls and for the
    $L^2$-risk. For this purpose, all possible models are divided into three
    groups: {\it uniform}, {\it regular} and {\it irregular}. We formulate the
    conditions when each of these situations takes place.

Math-arch

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