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Fadoua Balabdaoui

  1. Chernoff's density is log-concave.

    Втр, 03/06/2012 - 15:01 — SomNambul
    Authors: Fadoua Balabdaoui, Jon A. Wellner
    Subjects: Statistics
    Abstract

    We show that the density of $Z = \argmax \{W(t) - t^2 \}$, sometimes known as
    Chernoff's density, is log-concave. We conjecture that Chernoff's density is
    strongly log-concave or "super-Gaussian", and provide evidence in support of
    the conjecture. We also show that the standard normal density can be written in
    the same structural form as Chernoff's density, make connections with L.
    Bondesson's class of hyperbolically completely monotone densities, and identify
    a large sub-class thereof having log-transforms to $\RR$ which are strongly
    log-concave.

  2. Maximum likelihood estimation and confidence bands for a discrete log-concave distribution.

    Чт, 07/21/2011 - 15:01 — SomNambul
    Authors: Fadoua Balabdaoui, Kaspar Rufibach, Hanna Jankowski
    Subjects: Methodology
    Abstract

    The assumption of log-concavity is an attractive and flexible nonparametric
    shape constraint in distribution modelling. In this work, we study the maximum
    likelihood estimator (MLE) of a log-concave probability mass function. We show
    that the MLE is strongly consistent and derive pointwise asymptotic theory,
    which is used to calculate confidence bands for the true probability mass
    function. The proposed estimator and associated confidence bands may be easily
    computed using the R package logcondiscr.

  3. Efficient computation of the cdf of the maximal difference between Brownian bridge and its concave majorant.

    Втр, 05/11/2010 - 15:01 — SomNambul
    Authors: Fadoua Balabdaoui, Karim Filali
    Subjects: Computation
    Abstract

    In this paper, we describe two computational methods for calculating the
    cumulative distribution function and the upper quantiles of the maximal
    difference between a Brownian bridge and its concave majorant. The first method
    has two different variants that are both based on a Monte Carlo approach,
    whereas the second uses the Gaver-Stehfest (GS) algorithm for numerical
    inversion of Laplace transform.

  4. Least Squares estimation of two ordered monotone regression curves.

    Втр, 10/20/2009 - 12:53 — SomNambul
    Authors: Fadoua Balabdaoui, Filippo Santambrogio, Kaspar Rufibach
    Subjects: Methodology
    Abstract

    In this paper, we consider the problem of finding the Least Squares
    estimators of two isotonic regression curves $g^\circ_1$ and $g^\circ_2$ under
    the additional constraint that they are ordered; e.g., $g^\circ_1 \le
    g^\circ_2$.

  5. The distribution of the maximal difference between Brownian bridge and its concave majorant.

    Пнд, 10/05/2009 - 20:24 — SomNambul
    Authors: Jim Pitman, Fadoua Balabdaoui
    Subjects: Statistics
    Abstract

    We provide a representation of the maximal difference between a standard
    Brownian bridge and its concave majorant on the unit interval, from which we
    deduce expressions for the distribution and density functions and moments of
    this difference. This maximal difference has an application in nonparametric
    statistics where it arises in testing monotonicity of a density or regression
    curve.

  6. The distribution of the maximal difference between Brownian bridge and its concave majorant.

    Пнд, 10/05/2009 - 20:24 — SomNambul
    Authors: Jim Pitman, Fadoua Balabdaoui
    Subjects: Statistics
    Abstract

    We provide a representation of the maximal difference between a standard
    Brownian bridge and its concave majorant on the unit interval, from which we
    deduce expressions for the distribution and density functions and moments of
    this difference. This maximal difference has an application in nonparametric
    statistics where it arises in testing monotonicity of a density or regression
    curve.

  7. On the Grenander estimator at zero.

    Пт, 09/11/2009 - 19:12 — SomNambul
    Authors: Fadoua Balabdaoui, Hanna K. Jankowski, Marios Pavlides, Arseni Seregin, Jon A. Wellner
    Subjects: Statistics
    Abstract

    We establish limit theory for the Grenander estimator of a monotone density
    near zero. In particular we consider the situation when the true density $f_0$
    is unbounded at zero, with different rates of growth to infinity. In the course
    of our study we develop new switching relations by use of tools from convex
    analysis. The theory is applied to a problem involving mixtures.

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