2,101 research outputs found
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
Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator
AMS classifications: 62G20, 62G32;asymptotic normality;confidence intervals;Edgeworth expansions;extreme value index;Hill estimator;regular variation;tail index
Unbiased Tail Estimation by an Extension of the Generalized Pareto Distribution
AMS classifications: 62G20; 62G32;bias;exchange rate;heavy tails;peaks-over-threshold;regular variation;tail index
Mandelbrot's Extremism
In the sixties Mandelbrot already showed that extreme price swings are more likely than some of us think or incorporate in our models.A modern toolbox for analyzing such rare events can be found in the field of extreme value theory.At the core of extreme value theory lies the modelling of maxima over large blocks of observations and of excesses over high thresholds.The general validity of these models makes them suitable for out-of-sample extrapolation.By way of illustration we assess the likeliness of the crash of the Dow Jones on October 19, 1987, a loss that was more than twice as large as on any other single day from 1954 until 2004.exceedances;extreme value theory;heavy tails;maxima
An M-Estimator for Tail Dependence in Arbitrary Dimensions
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.asymptotic statistics;factor model;M-estimation;multivariate extremes;tail dependence
Projection Estimates of Constrained Functional Parameters
AMS classifications: 62G05; 62G07; 62G08; 62G20; 62G32;estimation;convex function;extreme value copula;Pickands dependence function;projection;shape constraint;support function;tangent cone
Inference on the tail process with application to financial time series modelling
To draw inference on serial extremal dependence within heavy-tailed Markov
chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed
nonparametric estimators of the spectral tail process. The methodology can be
extended to the more general setting of a stationary, regularly varying time
series. The large-sample distribution of the estimators is derived via
empirical process theory for cluster functionals. The finite-sample performance
of these estimators is evaluated via Monte Carlo simulations. Moreover, two
different bootstrap schemes are employed which yield confidence intervals for
the pre-asymptotic spectral tail process: the stationary bootstrap and the
multiplier block bootstrap. The estimators are applied to stock price data to
study the persistence of positive and negative shocks.Comment: 22 page
Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials
Many applications in risk analysis, especially in environmental sciences,
require the estimation of the dependence among multivariate maxima. A way to do
this is by inferring the Pickands dependence function of the underlying
extreme-value copula. A nonparametric estimator is constructed as the sample
equivalent of a multivariate extension of the madogram. Shape constraints on
the family of Pickands dependence functions are taken into account by means of
a representation in terms of a specific type of Bernstein polynomials. The
large-sample theory of the estimator is developed and its finite-sample
performance is evaluated with a simulation study. The approach is illustrated
by analyzing clusters consisting of seven weather stations that have recorded
weekly maxima of hourly rainfall in France from 1993 to 2011
Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator
AMS classifications: 62G20, 62G32;
Formation of a Metallic Contact: Jump to Contact Revisited
The transition from tunneling to metallic contact between two surfaces does
not always involve a jump, but can be smooth. We have observed that the
configuration and material composition of the electrodes before contact largely
determines the presence or absence of a jump. Moreover, when jumps are found
preferential values of conductance have been identified. Through combination of
experiments, molecular dynamics, and first-principles transport calculations
these conductance values are identified with atomic contacts of either
monomers, dimers or double-bond contacts.Comment: 4 pages, 5 figure
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