34,567 research outputs found
Relativistic Spheres
By analyzing the Einstein's equations for the static sphere, we find that
there exists a non-singular static configuration whose radius can approach its
corresponding horizon size arbitrarily.Comment: 8 pages revtex, 1 ps figur
Multiple Change-point Detection: a Selective Overview
Very long and noisy sequence data arise from biological sciences to social
science including high throughput data in genomics and stock prices in
econometrics. Often such data are collected in order to identify and understand
shifts in trend, e.g., from a bull market to a bear market in finance or from a
normal number of chromosome copies to an excessive number of chromosome copies
in genetics. Thus, identifying multiple change points in a long, possibly very
long, sequence is an important problem. In this article, we review both
classical and new multiple change-point detection strategies. Considering the
long history and the extensive literature on the change-point detection, we
provide an in-depth discussion on a normal mean change-point model from aspects
of regression analysis, hypothesis testing, consistency and inference. In
particular, we present a strategy to gather and aggregate local information for
change-point detection that has become the cornerstone of several emerging
methods because of its attractiveness in both computational and theoretical
properties.Comment: 26 pages, 2 figure
Fixed-domain asymptotic properties of tapered maximum likelihood estimators
When the spatial sample size is extremely large, which occurs in many
environmental and ecological studies, operations on the large covariance matrix
are a numerical challenge. Covariance tapering is a technique to alleviate the
numerical challenges. Under the assumption that data are collected along a line
in a bounded region, we investigate how the tapering affects the asymptotic
efficiency of the maximum likelihood estimator (MLE) for the microergodic
parameter in the Mat\'ern covariance function by establishing the fixed-domain
asymptotic distribution of the exact MLE and that of the tapered MLE. Our
results imply that, under some conditions on the taper, the tapered MLE is
asymptotically as efficient as the true MLE for the microergodic parameter in
the Mat\'ern model.Comment: Published in at http://dx.doi.org/10.1214/08-AOS676 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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