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Hanna K. Jankowski

  1. Confidence Regions for Means of Random Sets using Oriented Distance Functions.

    Чт, 06/09/2011 - 15:01 — SomNambul
    Authors: Hanna K. Jankowski, Larissa I. Stanberry
    Subjects: Methodology
    Abstract

    Image analysis frequently deals with shape estimation and image
    reconstruction. The ob jects of interest in these problems may be thought of as
    random sets, and one is interested in finding a representative, or expected,
    set. We consider a definition of set expectation using oriented distance
    functions and study the properties of the associated empirical set. Conditions
    are given such that the empirical average is consistent, and a method to
    calculate a confidence region for the expected set is introduced. The proposed
    method is applied to both real and simulated data examples.

  2. Nonparametric estimation of a convex bathtub-shaped hazard function.

    Пт, 01/15/2010 - 16:01 — SomNambul
    Authors: Hanna K. Jankowski, Jon A. Wellner
    Subjects: Statistics
    Abstract

    In this paper, we study the nonparametric maximum likelihood estimator (MLE)
    of a convex hazard function. We show that the MLE is consistent and converges
    at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is
    positive and strictly convex. Moreover, we establish the pointwise asymptotic
    distribution theory of our estimator under these same assumptions. One notable
    feature of the nonparametric MLE studied here is that no arbitrary choice of
    tuning parameter (or complicated data-adaptive selection of the tuning
    parameter) is required.

  3. Estimation of a discrete monotone distribution.

    Втр, 10/20/2009 - 12:53 — SomNambul
    Authors: Hanna K. Jankowski, Jon A. Wellner
    Subjects: Statistics
    Abstract

    We study and compare three estimators of a discrete monotone distribution:
    (a) the (raw) empirical estimator; (b) the "method of rearrangements"
    estimator; and (c) the maximum likelihood estimator. We show that the maximum
    likelihood estimator strictly dominates both the rearrangement and empirical
    estimators in cases when the distribution has intervals of constancy.

  4. 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.

Math-arch

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