Hanna K. Jankowski
Confidence Regions for Means of Random Sets using Oriented Distance Functions.
Thu, 06/09/2011 - 15:01 — SomNambulAuthors: Hanna K. Jankowski, Larissa I. Stanberry
Subjects: Methodology
AbstractImage 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.Nonparametric estimation of a convex bathtub-shaped hazard function.
Fri, 01/15/2010 - 16:01 — SomNambulAuthors: Hanna K. Jankowski, Jon A. Wellner
Subjects: Statistics
AbstractIn 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.Estimation of a discrete monotone distribution.
Tue, 10/20/2009 - 12:53 — SomNambulAuthors: Hanna K. Jankowski, Jon A. Wellner
Subjects: Statistics
AbstractWe 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.On the Grenander estimator at zero.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Fadoua Balabdaoui, Hanna K. Jankowski, Marios Pavlides, Arseni Seregin, Jon A. Wellner
Subjects: Statistics
AbstractWe 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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