A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e−|t| p and symmetric p-stable random variables, where p ∈ (0, 2]. We obtain various sharp moment an...

A first-order autoregressive process with inverse gaussian marginals is introduced. The innovation distributions are obtained under certain special cases. The unknown parameters are estimated using different methods and these estimators are shown to be consistent and asymptotically normal. The behavior of the estimators for small samples is studied through simulation experiments. On Sums of Tri...

This paper considers the problem of estimating the parameters of two-dimensional moving average random elds. We rst address the problem of expressing the covariance matrix of a moving average random eld, in terms of the model parameters. Assuming the random eld is Gaussian, we derive a closed form expression for the Cramer-Rao lower bound on the error variance in jointly estimating the model pa...

We examine the hypothesis of an increase of humus disintegration by analyzing chemical substances measured in the seepage water of a German forest. Problems arise because of a large percentage of missing observations. We use a regression model with spatial and temporal effects constructed in an exploratory data analysis. Spatial dependencies are modelled by random effects and an autoregressive ...

x Introduction Literature Review Dissertation Organization and Contribution Abbreviations Array Signal Processing Fundamentals and Current Approaches Problem Formulation Maximum Likelihood DOA Estimation with Gaussian Distributions The Stochastic Maximum Likelihood Method The Deterministic Maximum Likelihood Method The Deterministic Cram er Rao Bound for Gaussian Noise Subspace Based DOA Estima...

A vector autoregressive model allowing for unit roots as well as explosive characteristic roots is developed. The Granger-Johansen representation shows that this results in processes with two common features: a random walk and an explosively growing process. Co-integrating and co-explosive vectors can be found which eliminate these common factors. Likelihood ratio tests for linear restrictions ...

In this paper we combine the appealing properties of the stable Paretian distribution to model the heavy tails and the GARCH model to capture the phenomenon of the volatility clustering. We assume the asset-returns to have a particular multivariate stable distribution, i.e., to be sub-Gaussian random vectors. In this way the characteristic function has a tractable expression and the density fun...

This technical report summarizes a number of results for the multivariate t distribution which can exhibit heavier tails than the Gaussian distribution. It is shown how t random variables can be generated, the probability density function (pdf) is derived, and marginal and conditional densities of partitioned t random vectors are presented. Moreover, a brief comparison with the multivariate Gau...

A generalization of the correlation integral of Grassberger and Procaccia is used to develop a statistic that has the property that it is asymptotically zero if and only if the underlying Gaussian process is independent. The same implication also holds for certain related processes. It is shown that the stastistic is asymptotically normal for weakly dependent stationary processes. An example is...