4,066 research outputs found
Smooth tail index estimation
Both parametric distribution functions appearing in extreme value theory -
the generalized extreme value distribution and the generalized Pareto
distribution - have log-concave densities if the extreme value index gamma is
in [-1,0]. Replacing the order statistics in tail index estimators by their
corresponding quantiles from the distribution function that is based on the
estimated log-concave density leads to novel smooth quantile and tail index
estimators. These new estimators aim at estimating the tail index especially in
small samples. Acting as a smoother of the empirical distribution function, the
log-concave distribution function estimator reduces estimation variability to a
much greater extent than it introduces bias. As a consequence, Monte Carlo
simulations demonstrate that the smoothed version of the estimators are well
superior to their non-smoothed counterparts, in terms of mean squared error.Comment: 17 pages, 5 figures. Slightly changed Pickand's estimator, added some
more introduction and discussio
Tail index estimation, concentration and adaptivity
This paper presents an adaptive version of the Hill estimator based on
Lespki's model selection method. This simple data-driven index selection method
is shown to satisfy an oracle inequality and is checked to achieve the lower
bound recently derived by Carpentier and Kim. In order to establish the oracle
inequality, we derive non-asymptotic variance bounds and concentration
inequalities for Hill estimators. These concentration inequalities are derived
from Talagrand's concentration inequality for smooth functions of independent
exponentially distributed random variables combined with three tools of Extreme
Value Theory: the quantile transform, Karamata's representation of slowly
varying functions, and R\'enyi's characterisation of the order statistics of
exponential samples. The performance of this computationally and conceptually
simple method is illustrated using Monte-Carlo simulations
On Tail Index Estimation based on Multivariate Data
This article is devoted to the study of tail index estimation based on i.i.d.
multivariate observations, drawn from a standard heavy-tailed distribution,
i.e. of which 1-d Pareto-like marginals share the same tail index. A
multivariate Central Limit Theorem for a random vector, whose components
correspond to (possibly dependent) Hill estimators of the common shape index
alpha, is established under mild conditions. Motivated by the statistical
analysis of extremal spatial data in particular, we introduce the concept of
(standard) heavy-tailed random field of tail index alpha and show how this
limit result can be used in order to build an estimator of alpha with small
asymptotic mean squared error, through a proper convex linear combination of
the coordinates. Beyond asymptotic results, simulation experiments illustrating
the relevance of the approach promoted are also presented
Selection index estimation from partial multivariate normal data
Selection index estimation from partial multivariate normal dat
Semiparametric Lower Bounds for Tail Index Estimation
indexation;semiparametric estimation
Modulation-Index Estimation in a Combined CPM/OFDM Receiver
In this paper we develop a blind modulation-index estimator for\ud
a combined CPM/OFDMReceiver. The performance of the estimator\ud
in an AWGN channel is assessed by simulation and analysis\ud
and its suitability for our receiver is established
High-Frequency Tail Index Estimation by Nearly Tight Frames
This work develops the asymptotic properties (weak consistency and
Gaussianity), in the high-frequency limit, of approximate maximum likelihood
estimators for the spectral parameters of Gaussian and isotropic spherical
random fields. The procedure we used exploits the so-called mexican needlet
construction by Geller and Mayeli in [Geller, Mayeli (2009)]. Furthermore, we
propose a plug-in procedure to optimize the precision of the estimators in
terms of asymptotic variance.Comment: 38 page
Multifidelity variance reduction for pick-freeze Sobol index estimation
Many mathematical models involve input parameters, which are not precisely
known. Global sensitivity analysis aims to identify the parameters whose
uncertainty has the largest impact on the variability of a quantity of interest
(output of the model). One of the statistical tools used to quantify the
influence of each input variable on the output is the Sobol sensitivity index,
which can be estimated using a large sample of evaluations of the output. We
propose a variance reduction technique, based on the availability of a fast
approximation of the output, which can enable significant computational savings
when the output is costly to evaluate
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