In this paper we derive computable expressions for the likelihood ratio for Gaussian processes with a discrete two-dimensional parameter domain (for instance, an image). A general formula for the likelihood ratio can be easily derived, but becomes inefficient if the number of elements in the...

We consider the problem of estimating the location and size of a discontinuity in an otherwise smooth multidimensional regression function. The boundary or location of the discontinuity is assumed to be a closed curve respective surface, and we aim to estimate this closed set. Our approach...

The distribution of a positive quadratic form of an infinite Gaussian sequence is investigated. Equivalently, the law of X + a2 is described, where X is a symmetric Gaussian random variable taking values in a Hilbert space H and a [set membership, variant] H. It is shown that X + a2 =dX2 +...

Based on the concept of complexity or minimum description length developed by Kolmogorov, Rissanen, Wallace, and others, an index of predictive power is proposed as a criterion to select the principal components of a random vector distributed in a parametric family. This criterion, when applied...

The choice of a matrix square root in order to define a correlation coefficient is crucial for the notion of partial autocorrelation function (PACF) for a multivariate time series. Here this topic is revisited and, introducing a new matrix link coefficient between two random vectors, a general...

We consider the MDS problem of fitting an lp-distance matrix to a given dissimilarity matrix with respect to the weighted least squares loss function (STRESS). The problem is reduced to the maximization of a ratio of two norms on a finite dimensional Hilbert space. A necessary condition for a...

This paper extends the results of Chen and Wu [1] concerning consistency of M-estimators in the linear regression model. We consider M-estimators defined by [formula] in the general regression model yi = f(xi,[theta] ) + [epsilon]i, where f(x, [theta]) is continuous on a separable metric space X...

The purpose of this paper is to extend the class of AR(1) models introduced by Aly and Bouzar (1994) to more general ARMA models. As an application some new Poisson geometric, negative binomial, and Poisson logarithmic ARMA models are derived.

In some long term medical follow-up studies, a series of dependent and possibly censored failure times may be observed. Suppose that these failure times were generated from the same distribution function, and inferences about it are of our main interest. In this article, we show that under...

The Kotz-type distributions form an important class of multivariate elliptical distributions. These distributions are studied in Fang et al. [Symmetric Multivariate and Related Distributions, Chap. 3.2. Chapman and Hall, London]. In the particular case when the shape parameters s equals 1,...