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Adaptive estimation in regression and complexity of approximation of random fields
regression and complexity approximation random fields
2012/9/17
In this thesis we study adaptive nonparametric regression with noise misspecifi-cation and the complexity of approximation of random fields in dependence of the dimension.
First, we consider the prob...
Polar sets of anisotropic Gaussian random fields
Anisotropic Gaussian fields Hitting probabilities Polar sets Hausdorff dimension European option Jump diffusion Calibration
2012/9/18
This paper studies polar sets of anisotropic Gaussian random fields,i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance ...
Detecting sparse cone alternatives for Gaussian random fields, with an application to fMRI
random elds Euler characteristic kinematic formulae volumes of tubes expansion order-restricted inference multivari-ate one-sided hypotheses non-negative least squares.
2012/9/19
Our problem is to nd a good approximation to the P-value of the maximum of a random eld of test statistics for a cone alternative at each point in a sample of Gaussian random elds. These test stati...
Generalized Interference Models in Doubly Stochastic Poisson Random Fields for Wideband Communications: the PNSC(alpha) model
Interference models Cox Process Doubly Stochastic Poisson Stable Process Isotropicα-stable Complexα-stable
2012/9/19
A general stochastic model is developed for the total interference in wideband systems, denoted as the PNSC(α) Interference Model. It allows one to obtain, analytic representations in situations where...
The V/S test of long-range dependence in random fields
Long memory V/S statistic random fields
2009/9/16
Recently, Giraitis et al. (2003, [10]) proposed the $V/S$ statistic for testing long memory in random sequences. We generalize this statistic to the setting of random fields. The null hypothesis is co...