We study the estimation problem of the parameter of a stationary AR(p) process with infinite variance when there is no assumption on the causality of the model. We propose consistent estimates. In the causal case, we obtain a speed of convergence.

The Riemann space whose elements are m - k (m [greater, double equals] k) matrices X, i.e., orientations, such that X'X = Ik is called the Stiefel manifold Vk,m. The matrix Langevin (or von Mises-Fisher) and matrix Bingham distributions have been suggested as distributions on Vk,m. In this...

In Bhattacharya and Mack (Ann. Statist. 15 (1987), 976-994), it was shown (among other things) that adapting for the optimal choice of k in univariate k-nearest neighbor density and regression estimation is feasible using weak convergence techniques. We now show that the same holds true for the...

A new class of estimators is introduced for estimating the parameter ([theta]10, [theta]20) in the linear regression model y = E[YX = x] = [theta]10 + [theta]20x. Given independent copies {(X1, Y1),..., (Xn, Yn)} of the two-dimensional random vector (X, Y), these estimators are derived from...

Performance of the bootstrap for estimating tail probabilities is usually explained by saying that the bootstrap provides a one-term Edgeworth correction. However, simulation studies show that the bootstrap usually performs better than explicit Edgeworth correction. We present a theory which...

Orderings (denoted ) for probability distributions on the circle are introduced for which [mu]1 [mu]2 means roughly that [mu]1 is "more uniform" than [mu]2, or that [mu]2 is "more clumped" than [mu]1. Somewhat more precisely, [mu]1 [mu]2 if the random variable [mu]1(As) is "less variable" than...

Bilinear models which are defined as input-output (noise-observation in time series analysis) systems being linear with respect to each of the input and output when the other is fixed, arise in a natural way from basic principles in chemistry, physics, engineering, and several other fields of...

A stochastic integral with respect to a generalized, i.e., not necessarily time-homogeneous, Wiener process in the dual of a nuclear space is defined. The integrands are random linear operators X = (Xs)s[set membership, variant]R+, with values in the dual of a multi-Hilbertian space, the domain...

Given a statistical model for data which take values in Rd and have elliptically distributed errors, and affine equivariant estimators [mu] and [mu] of a mean vector in Rd[circle times operator]Rn and a d - d scatter matrix, expressions are given for the covarances of the estimators in terms of...

Using two kinds of multivariate regular variation we prove several Abel-Tauber theorems for the Laplace transform of functions in several variables. We generalize some power series results of Alpar and apply our results in multivariate renewal theory.