In random truncation models one observes the i.i.d. pairs (Ti[less-than-or-equals, slant]Yi),i=1, ..., n. IfYis the variable of interest, thenTis another independent variable which prevents the complete observation ofYand random left truncation occurs. Such a type of incomplete data is...

In this paper we discuss set-valued stationary processes. First, we prove a stationary selection and representation theorem, then we study the laws of large numbers and ergodicities of set-valued stationary processes.

Pairwise linear discriminant analysis ofmpopulations inRncan be regarded as a process to generate rankings of the populations. Whennis small compared withm, some of them! rankings are not generated. We give formulae for the number of generated rankings. Moreover, we give basic characterizations...

Suppose a number of points are deleted from a sample of random vectors in d. The number of deleted points may depend on the sample sizen, and on any other sample information, provided only that it is bounded in probability asn--[infinity]. In particular, "extremes" of the sample, however...

In this paper, we study the weak convergence of Dirichlet measures on the class constituted by vectors of subprobability measures such that the sum of its components is a probability measure on a complete separable metric space. This vectorial class of subprobabilities appears in the context of...

Let (X, B, Y) denote a random vector such thatBandYare real-valued, andX[set membership, variant]2. Local linear estimates are used in the partial regression method for estimating the regression functionE(Y|X, B)=[alpha]B+m(X), where[alpha]is an unknown parameter, andm(·) is a smooth...

We consider a linear normal modelY=X[theta]+ewith[theta]verifying a linear restriction and the standard estimators [theta](unrestricted MLE) and[theta]* (restricted MLE). We prove that[theta]* is preferable to [theta]using a new and strong criterion which implies the domination under other usual...

Suppose thatX~N-m([mu], [Sigma], [Theta]). An expression for the density function is given when[Sigma][greater-or-equal, slanted]0 and/or[Theta]:[greater-or-equal, slanted]0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a matrixZof...

An approximate degrees of freedom test is suggested for hypotheses of the kindH0:C'[Phi]1M=C'[Phi]2Min two independent multivariate linear models:Yi=Xi i[Phi]i+[var epsilon]i,i=1, 2, under the assumption of error matrix variate normality and heteroscedasticity. It is shown for specific vector...