Ethan Anderes
A general spline representation for nonparametric and semiparametric density estimates using diffeomorphisms.
Fri, 05/25/2012 - 15:01 — SomNambulAuthors: Ethan Anderes, Marc Coram
Subjects: Methodology
AbstractA theorem of McCann shows that for any two absolutely continuous probability
measures on R^d there exists a monotone transformation sending one probability
measure to the other. A consequence of this theorem, relevant to statistics, is
that density estimation can be recast in terms of transformations. In
particular, one can fix any absolutely continuous probability measure, call it
P, and then reparameterize the whole class of absolutely continuous probability
measures as monotone transformations from P.Local likelihood estimation of local parameters for nonstationary random fields.
Tue, 11/03/2009 - 16:01 — SomNambulAuthors: Ethan Anderes, Michael Stein
Subjects: Methodology
AbstractWe develop a weighted local likelihood estimate for the parameters that
govern the local spatial dependency of a locally stationary random field. The
advantage of this local likelihood estimate is that it smoothly downweights the
influence of far away observations, works for irregular sampling locations, and
when designed appropriately, can trade bias and variance for reducing
estimation error. This paper starts with an exposition of our technique on the
problem of estimating an unknown positive function when multiplied by a
stationary random field.Consistent estimates of deformed isotropic Gaussian random fields on the plane.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: Sourav Chatterjee, Ethan Anderes
Subjects: gr. Statistics
AbstractThis paper proves fixed domain asymptotic results for estimating a smooth
invertible transformation $f:\Bbb{R}^2\to\Bbb{R}^2$ when observing the deformed
random field $Z\circ f$ on a dense grid in a bounded, simply connected domain
$\Omega$, where $Z$ is assumed to be an isotropic Gaussian random field on
$\Bbb{R}^2$. The estimate $\hat{f}$ is constructed on a simply connected domain
$U$, such that $\overline{U}\subset\Omega$ and is defined using kernel smoothed
quadratic variations, Bergman projections and results from quasiconformal
theory.
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