5,600 research outputs found
General empirical Bayes wavelet methods and exactly adaptive minimax estimation
In many statistical problems, stochastic signals can be represented as a
sequence of noisy wavelet coefficients. In this paper, we develop general
empirical Bayes methods for the estimation of true signal. Our estimators
approximate certain oracle separable rules and achieve adaptation to ideal
risks and exact minimax risks in broad collections of classes of signals. In
particular, our estimators are uniformly adaptive to the minimum risk of
separable estimators and the exact minimax risks simultaneously in Besov balls
of all smoothness and shape indices, and they are uniformly superefficient in
convergence rates in all compact sets in Besov spaces with a finite secondary
shape parameter. Furthermore, in classes nested between Besov balls of the same
smoothness index, our estimators dominate threshold and James-Stein estimators
within an infinitesimal fraction of the minimax risks. More general block
empirical Bayes estimators are developed. Both white noise with drift and
nonparametric regression are considered.Comment: Published at http://dx.doi.org/10.1214/009053604000000995 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamic density estimation with diffusive Dirichlet mixtures
We introduce a new class of nonparametric prior distributions on the space of
continuously varying densities, induced by Dirichlet process mixtures which
diffuse in time. These select time-indexed random functions without jumps,
whose sections are continuous or discrete distributions depending on the choice
of kernel. The construction exploits the widely used stick-breaking
representation of the Dirichlet process and induces the time dependence by
replacing the stick-breaking components with one-dimensional Wright-Fisher
diffusions. These features combine appealing properties of the model, inherited
from the Wright-Fisher diffusions and the Dirichlet mixture structure, with
great flexibility and tractability for posterior computation. The construction
can be easily extended to multi-parameter GEM marginal states, which include,
for example, the Pitman--Yor process. A full inferential strategy is detailed
and illustrated on simulated and real data.Comment: Published at http://dx.doi.org/10.3150/14-BEJ681 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Statistical Model of Shape Moments with Active Contour Evolution for Shape Detection and Segmentation
This paper describes a novel method for shape representation and robust image segmentation. The proposed method combines two well known methodologies, namely, statistical shape models and active contours implemented in level set framework. The shape detection is achieved by maximizing a posterior function that consists of a prior shape probability model and image likelihood function conditioned on shapes. The statistical shape model is built as a result of a learning process based on nonparametric probability estimation in a PCA reduced feature space formed by the Legendre moments of training silhouette images. A greedy strategy is applied to optimize the proposed cost function by iteratively evolving an implicit active contour in the image space and subsequent constrained optimization of the evolved shape in the reduced shape feature space. Experimental results presented in the paper demonstrate that the proposed method, contrary to many other active contour segmentation methods, is highly resilient to severe random and structural noise that could be present in the data
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