A linear functional errors-in-variables model with unknown slope parameter and Gaussian errors is considered. The measurement error variance is supposed to be known, while the variance of errors in the equation is unknown. In this model a risk bound of asymptotic minimax type for arbitrary...

Fixed point clustering is a new stochastic approach to cluster analysis. The definition of a single fixed point cluster (FPC) is based on a simple parametric model, but there is no parametric assumption for the whole dataset as opposed to mixture modeling and other approaches. An FPC is defined...

The problem of estimating a mean vector of scale mixtures of multivariate normal distributions with the quadratic loss function is considered. For a certain class of these distributions, which includes at least multivariate-t distributions, admissible minimax estimators are given.

The least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of...

The paper presents asymptotic distributions of [phi]-disparity goodness-of-fit statistics in product multinomial models, under hypotheses and alternatives assuming sparse and nonsparse cell frequencies. The [phi]-disparity statistics include the power divergences of Read and Cressie...

The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function...

This paper concerns the matrix Langevin distributions, exponential-type distributions defined on the two manifolds of our interest, the Stiefel manifold Vk,m and the manifold Pk,m-k of mxm orthogonal projection matrices idempotent of rank k which is equivalent to the Grassmann manifold Gk,m-k....

De Finetti style theorems characterize models (predictive distributions) as mixtures of the likelihood function and the prior distribution, beginning from some judgment of invariance about observable quantities. The likelihood function generally has its functional form identified from invariance...

Consider a stochastic sequence {Zn; n=1,2,...}, and define Pn([var epsilon])=P(Zn<[var epsilon]). Then the stochastic convergence Zn-->0 is said to be monotone whenever the sequence Pn([var epsilon])[short up arrow]1 monotonically in n for each [var epsilon]0. This mode of convergence is investigated here; it is seen to be stronger than convergence...</[var>

Deepest regression (DR) is a method for linear regression introduced by P. J. Rousseeuw and M. Hubert (1999, J. Amer. Statis. Assoc.94, 388-402). The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with...