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Asymptotic results for sample autocovariance functions and extremes of integrated generalized Ornstein-Uhlenbeck processes
continuous-time GARCH process extreme value theory generalizedOrnstein–Uhlenbeck process integrated generalized Ornstein–Uhlenbeck process
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2010/3/10
We consider a positive stationary generalized Ornstein–Uhlenbeck process
Vt = e−tZ t0es− ds + V0 for t 0,and the increments of the integrated generalized Ornstein–Uhlenbeck process...
Large deviations for extremes of U-processes
Large deviations extremes of U-processes
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2009/9/22
We prove a large deviations principle (LDP) for partial
sums U-processes indexed by the half line. The LDP can be formulated
on a suitable subset of the set of all absolutely continuous paths. We
e...
Expansions for Quantiles and Multivariate Moments of Extremes for Distributions of Pareto Type
Bell polynomials Extremes Inversion theorem Moments Pareto Quantiles
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2010/3/19
Let Xnr be the rth largest of a random sample of size n from a distribution
F(x) = 1 −P∞i=0 cix− −i for > 0 and > 0. An inversion theorem is proved and used to
derive an expan...
Extremes of Levy processes with light tails
Poisson process Brownian motion supremum
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2010/3/18
Let X(t) t 0 ,X(0) = 0, be a L´evy process with spectral L´evy measure . Assuming that ((−1, 0)) < 1 and the right tail of is light, we show that in the presence of Brownian co...
Statistics of extremes by oracle estimation
Nonparametric adaptive estimation extreme values Hill estimator probabilities of rare events high quantiles
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2010/4/30
We use the fitted Pareto law to construct an accompanying approximation
of the excess distribution function. A selection rule of
the location of the excess distribution function is proposed based on...