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Dominique Picard

  1. Testing the isotropy of high energy cosmic rays using spherical needlets.

    Пт, 07/29/2011 - 15:01 — SomNambul
    Authors: Dominique Picard, Gilles Faÿ, Jacques Delabrouille, Gérard Kerkyacharyan
    Subjects: Applications
    Abstract

    For many decades, ultra-high energy charged particles have been a puzzle for
    particle physicists and astrophysicists. Nor the sites of production, nor the
    mechanism responsible for the generation of these ultra-energetic `cosmic rays'
    (CR) are currently known. They seem to arrive from random direction in the sky,
    although the most energetic ones, which are not deflected much by the magnetic
    fields, are supposed to point towards their source with good accuracy.

  2. Localized spherical deconvolution.

    Втр, 06/14/2011 - 15:01 — SomNambul
    Authors: Dominique Picard, Thanh Mai Pham Ngoc, Gérard Kerkyacharian
    Subjects: Statistics
    Abstract

    We provide a new algorithm for the treatment of the deconvolution problem on
    the sphere which combines the traditional SVD inversion with an appropriate
    thresholding technique in a well chosen new basis. We establish upper bounds
    for the behavior of our procedure for any $\mathbb {L}_p$ loss. It is important
    to emphasize the adaptation properties of our procedures with respect to the
    regularity (sparsity) of the object to recover as well as to inhomogeneous
    smoothness. We also perform a numerical study which proves that the procedure
    shows very promising properties in practice as well.

  3. A new selection method for high-dimensionial instrumental setting: application to the Growth Rate convergence hypothesis.

    Втр, 03/22/2011 - 16:01 — SomNambul
    Authors: Dominique Picard, Mathilde Mougeot, Karine Tribouley
    Subjects: Statistics
    Abstract

    This paper investigates the problem of selecting variables in regression-type
    models for an "instrumental" setting. Our study is motivated by empirically
    verifying the conditional convergence hypothesis used in the economical
    literature concerning the growth rate. To avoid unnecessary discussion about
    the choice and the pertinence of instrumental variables, we embed the model in
    a very high dimensional setting. We propose a selection procedure with no
    optimization step called LOLA, for Learning Out of Leaders with Adaptation.
    LOLA is an auto-driven algorithm with two thresholding steps.

  4. Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds.

    Втр, 02/15/2011 - 16:01 — SomNambul
    Authors: Gerard Kerkyacharian, Dominique Picard, Richard Nickl
    Subjects: Statistics
    Abstract

    Let $X_1,...,X_n$ be a random sample from some unknown probability density
    $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge
    1$. Consider a 'needlet frame' $\{\phi_{j \eta}\}$ describing a localised
    projection onto the space of eigenfunctions of the Laplace operator on $\mathbf
    M$ with corresponding eigenvalues less than $2^{2j}$, as constructed in
    \cite{GP10}.

  5. Learning Out of Leaders.

    Ср, 01/13/2010 - 16:01 — SomNambul
    Authors: Gerard Kerkyacharian, Dominique Picard, Mathilde Mougeot, Karine Tribouley
    Subjects: Statistics
    Abstract

    This paper investigates the problem of selection and estimation in a high
    dimensional regression-type model. We propose a procedure with no optimization
    called LOL, for Learning Out of Leaders. LOL is an auto-driven algorithm with
    two thresholding steps. A first adaptive thresholding helps to select leaders
    among the initial regressors in such a way to reduce the dimensionality. Then a
    second thresholding follows the estimations and predictions performed by linear
    regression on the leaders. Theoretical results are proved.

  6. Radon needlet thresholding.

    Ср, 08/19/2009 - 19:30 — SomNambul
    Authors: Gerard Kerkyacharian, Erwan Le Pennec, Dominique Picard
    Subjects: gr. Statistics
    Abstract

    We provide a new algorithm for the treatment of the noisy inversion of the
    radon transform using an appropriate thresholding technique adapted to a well
    chosen new localized basis. We establish minimax results and prove their
    optimality. In particular we prove that the procedures provided here are able
    to attain minimax bounds for any $\bL_p$ loss. It is important to notice that
    most of the minimax bounds obtained here are new to our knowledge.

Math-arch

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