From the results of convergence by sampling in linear principal component analysis (of a random function in a separable Hilbert space), the limiting distribution is given for the principal values and the principal factors. These results can be explicitly written in the normal case. Some...

It is shown that every genuinely d-dimensional distribution of class L on Rd is absolutely continuous. This extends the known fact in one dimension to all finite dimensions.

The least absolute deviation estimates L(N), from N data points, of the autoregressive constants a = (a1, ..., aq)' for a stationary autoregressive model, are shown to have the property that N[sigma](L(N) - a) converge to zero in probability, for [sigma] 1/[alpha], where the disturbances are...

Let (T1, x1), (T2, x2), ..., (Tn, xn) be a sample from a multivariate normal distribution where Ti are (unobservable) random variables and xi are random vectors in Rk. If the sample is either independent and identically distributed or satisfies a multivariate components of variance model, then...

This paper indicates a mixing condition under which a net of Fourier transforms, of a stationary generalized process over an abelian locally compact group, has a limiting normal distribution.

A general theory of concepts of positive dependence, which are weaker than association but stronger than orthant dependence, is developed. A random vector X is associated if and only if P(X [set membership, variant] A [down curve] B) = P(X [set membership, variant] A) P(X [set membership,...

The paper is devoted to metrization of probability spaces through the introduction of a quadratic differential metric in the parameter space of the probability distributions. For this purpose, a [phi]-entropy functional is defined on the probability space and its Hessian along a direction of the...

Almost sure convergence properties of least-squares estimates in stochastic regression models and an asymptotic theory of related Euclidean projections are developed herein. Applications to autoregressive processes and to dynamic input-output systems are also discussed.

For some general multivariate linear models, linear rank statistics are used in conjunction with Roy's Union-Intersection Principle to develop some tests for inference on the parameter (vector) when they are subject to certain linear constraints. More powerful tests are designed by incorporating...

Two related almost sure limit theorems are obtained in connection with a stochastic process {[xi](t), -[infinity] < t < [infinity]} with independent increments. The first result deals with the existence of a simultaneous stabilizing function H(t) such that ([xi](t) - [xi](0))/H(t) --> 0 for almost all sample functions of the process. The second result deals with a wide-sense stationary process whose random spectral distributions is [xi]. It addresses the...</t>