752 research outputs found
Moderate deviation probabilities for open convex sets: nonlogarithmic behavior
Precise asymptotics for moderate deviation probabilities are established for
open convex sets in both the finite- and infinite-dimensional settings.
Our results are based on the existence of dominating points for these sets, a
related representation formula, and asymptotics for the integral term in this
formula.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000021
Uniform in bandwidth consistency of kernel-type function estimators
We introduce a general method to prove uniform in bandwidth consistency of
kernel-type function estimators. Examples include the kernel density estimator,
the Nadaraya-Watson regression estimator and the conditional empirical process.
Our results may be useful to establish uniform consistency of data-driven
bandwidth kernel-type function estimators.Comment: Published at http://dx.doi.org/10.1214/009053605000000129 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A method of moments estimator of tail dependence
In the world of multivariate extremes, estimation of the dependence structure
still presents a challenge and an interesting problem. A procedure for the
bivariate case is presented that opens the road to a similar way of handling
the problem in a truly multivariate setting. We consider a semi-parametric
model in which the stable tail dependence function is parametrically modeled.
Given a random sample from a bivariate distribution function, the problem is to
estimate the unknown parameter. A method of moments estimator is proposed where
a certain integral of a nonparametric, rank-based estimator of the stable tail
dependence function is matched with the corresponding parametric version. Under
very weak conditions, the estimator is shown to be consistent and
asymptotically normal. Moreover, a comparison between the parametric and
nonparametric estimators leads to a goodness-of-fit test for the semiparametric
model. The performance of the estimator is illustrated for a discrete spectral
measure that arises in a factor-type model and for which likelihood-based
methods break down. A second example is that of a family of stable tail
dependence functions of certain meta-elliptical distributions.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ130 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Empirical Likelihood based on Hypothesis Testing
AMS classifications: 62G10; 62G20; 62G30;estimation;testing;likelihood
Ultimate 100m World Records Through Extreme-Value Theory
We use extreme-value theory to estimate the ultimate world records for the 100m running, for both men and women. For this aim we collected the fastest personal best times set between January 1991 and June 2008. Estimators of the extreme-value index are based on a certain number of upper order statistics. To optimize this number of order statistics we minimize the asymptotic mean squared error of the moment estimator. Using the thus obtained estimate for the extreme-value index, the right endpoint of the speed distribution is estimated. The corresponding time can be interpreted as the estimated ultimate world record: the best possible time that could be run in the near future. We find 9.51 seconds for the 100m men and 10.33 seconds for the women. Running title. Ultimate 100m world records.
Asymptotics for the Hirsch Index
The last decade methods for quantifying the research output of individual researchers have become quite popular in academic policy making. The h- index (Hirsch, 2005) constitutes an interesting quality measure that has attracted a lot of attention recently. It is now a standard measure available for instance on theWeb of Science. In this paper we establish the asymptotic normality of the empirical h-index. The rate of convergence is non-standard: ph=(1 + nf(h)), where f is the density of the citation distribution and n the number of publications of a researcher. In case that the citations follow a Pareto-type or a Weibull-type distribution as defined in extreme value theory, our general result nicely specializes to results that are useful for constructing confidence intervals for the h-index.Asymptotic normality;confidence interval;extreme value theory;research output;scientometrics;tail empirical process.
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