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For estimation and predictions of random fields it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate...
We introduce the notion of anisotropic long memory for random fields on $\mathbb{Z}^2$ whose partial sums on incommensurate rectangles with sides growing at different rates O(n) and $O(n^{H_1/H_2})$, ...
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...
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 ...
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...
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...
We consider the problem of training probabilistic conditional random fields (CRFs) in the context of a task where performance is measured using a specific loss function. While maximum likelihood is th...
We provide new methods for estimation of the one-point specification probabilities in general discrete random fields.
Ich erkl¨are ehrenw¨ortlich, dass ich die vorliegende Schrift verfasst und die mit ihr unmittelbar verbundenen Arbeiten selbst durchgef¨uhrt habe. Die in der Schrift verwendete Literatur sowie das A...
We consider Markov Random Fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. The formal definition of the...
Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when tho...
Sequential estimation in random fields
Minimax sequential estimation based on random fields
We study finite-dimensional distributions of symmetric a-stable (abbreviated as SuS) random fields of Chentsov type, 0 < a < 2. We discuss a structure of the spherical components of Uvy measures an...
We present the Marcinkiewicz-type strong law of large numbers for random fields {X,, n E Zd,) of pairwise independent random variables, where Zd,, d & 1, is the set of positive d-dimensional lattic...

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