How sharp are classical approximations for statistical applications
TLDR
This paper aims at comparing theoretical approximations of the tail of the maximum of stochastic processes and the corresponding numerical evaluations of the Pickands or double sum method, the Rice Method, the Euler Characteristic method and a new one called the Poisson method.Abstract:
This paper aims at comparing theoretical approximations of the tail of the maximum of stochastic processes and the corresponding numerical evaluations. More particularly, we focus on the Pickands or double sum method, the Rice method, the Euler Characteristic method and a new one called the Poisson method. The numerical evaluation, performed using mainly Quasi Monte-Carlo integration and adaptations of the programs of Genz, show the domains of validity of each method.read more
Citations
More filters
Posted Content
Geometry of conjunction set of smooth stationary Gaussian fields
Jean-Marc Azaïs,Viet-Hung Pham +1 more
TL;DR: In this paper, the authors investigated the conjunction probability that at a same point the values of the Gaussian fields exceed the given threshold. And they gave a partial validity of Euler characteristic method, using a recent result of Azai s and Wschebor describing the shape of the excursion set.
Posted Content
Asymptotic formula for the conjunction probability of smooth stationary Gaussian fields
TL;DR: In this paper, the authors derived an asymptotic formula for the conjunction probability of a stationary centered Gaussian field with smooth sample paths from the behavior of the volume of the set of local maximum points.
Journal ArticleDOI
Asymptotic formula for the conjunction probability of smooth stationary Gaussian fields
TL;DR: In this article , the authors derived an asymptotic formula for the conjunction probability of a stationary centered Gaussian field with smooth sample paths from the behavior of the volume of the set of local maximum points.
References
More filters
Book
Statistics for spatial data
Noel A Cressie,Noel A Cressie +1 more
TL;DR: In this paper, the authors present a survey of statistics for spatial data in the field of geostatistics, including spatial point patterns and point patterns modeling objects, using Lattice Data and spatial models on lattices.
Journal ArticleDOI
Mathematical analysis of random noise
TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Book
The Geometry of Random Fields
TL;DR: In this article, the authors present a survey of random fields and excursion sets and their spectral properties, including sample function regularity, sample function erraticism, and the Markov property for Gaussian fields.
Related Papers (5)
Laplaces method for gaussian integrals with an application to statistical-mechanics
Richard S. Ellis,Jay Rosen +1 more