Random fields of multivariate test statistics, with applications to shape analysis

Random Fields of Multivariate Test Statistics , with Applications to Shape Analysis

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are non-zero using classical multivariate statistics evaluated at each point. The problem is to find the P-value of the maximum of such a random field of test statistics. We ap...

Random Matrix Line Shape Theory with Applications to Lévy Statistics ∗

A model system of a bright state coupled to a manifold of dark states is analyzed with regard to the width distributions of the dark manifold induced in the bright state. Independent box shaped distributions are assumed for the energy distributions, the coupling distributions and the dark level width-distributions. The width distributions induced via the couplings from the dark levels into the ...

Random Projection-Based Anderson-Darling Test for Random Fields

In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R, and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior o...

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Markov Random Fields in Statistics