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Yvik Swan

  1. Optimal tests for the two-sample spherical location problem.

    Tue, 05/22/2012 - 15:01 — SomNambul
    Authors: Christophe Ley, Yvik Swan, Thomas Verdebout
    Subjects: Statistics
    Abstract

    We tackle the classical two-sample spherical location problem for directional
    data by having recourse to the Le Cam methodology, habitually used in classical
    "linear" multivariate analysis. More precisely we construct locally and
    asymptotically optimal (in the maximin sense) parametric tests, which we then
    turn into semi-parametric ones in two distinct ways. First, by using a
    studentization argument; this leads to so-called pseudo-FvML tests. Second, by
    resorting to the invariance principle; this leads to efficient rank-based
    tests.

  2. A remark on the ARE between Wilcoxon's and van~der~Waerden's scores.

    Tue, 11/22/2011 - 15:01 — SomNambul
    Authors: Yvik Swan, Camille Sabbah, Thomas Verdebout, Nadir Maaroufi
    Subjects: Statistics
    Abstract

    We provide an upper bound (together with the conditions under which this
    bound holds) on the asymptotic relative efficiency of the Wilcoxon rank-based
    test with respect to the van der Waerden rank-based test. Furthermore, we
    characterize the family of distributions under which the upper bound is
    achieved.

  3. On a connection between Stein characterizations and Fisher information.

    Fri, 11/11/2011 - 15:01 — SomNambul
    Authors: Christophe Ley, Yvik Swan
    Subjects: Probability
    Abstract

    We generalize the so-called density approach to Stein characterizations of
    probability distributions. We prove an elementary factorization property of the
    resulting Stein operator in terms of a generalized (standardized) score
    function. We use this result to connect Stein characterizations with
    information distances such as the generalized (standardized) Fisher
    information.

  4. Optimal R-Estimation of a Spherical Location.

    Mon, 09/26/2011 - 15:01 — SomNambul
    Authors: Baba Thiam, Christophe Ley, Yvik Swan, Thomas Verdebout
    Subjects: Applications
    Abstract

    In this paper, we provide R-estimators of the location of a rotationally
    symmetric distribution on the unit sphere of $R^k$. In order to do so we ?first
    prove the local asymptotic normality property of a sequence of rotationally
    symmetric models; this is a non standard result due to the curved nature of the
    unit sphere. We then construct our estimators by adapting the Le Cam one-step
    methodology to spherical statistics and ranks. We show that they are
    asymptotically normal under any rotationally symmetric distribution and achieve
    the efficiency bound under a specific density.

  5. Univariate and multivariate Chen-Stein characterizations -- a parametric approach.

    Thu, 05/26/2011 - 15:01 — SomNambul
    Authors: Christophe Ley, Yvik Swan
    Subjects: Probability
    Abstract

    We provide a general framework for characterizing families of (univariate,
    multivariate, discrete and continuous) distributions in terms of a parameter of
    interest. We show how this allows for recovering known Chen-Stein
    characterizations, and for constructing many more. Several examples are worked
    out in full, and different potential applications are discussed.

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