Table of contents, Bernoulli Journal, vol. 7, no. 3 (2001)

Asymptotics of the maximum likelihood estimator for general hidden Markov models; Authors: Randal Douc, Catherine Matias

On the effect of covariance function estimation on the accuracy of kriging predictors; Authors: Hein Putter, G. Alastair Young

On Gaussian and Bernoulli covariance representations; Authors: Sergey G. Bobkov, Friedrich Götze, Christian Houdré

Infinite hierarchies and prior distributions; Authors: Gareth O. Roberts, Jeffrey S. Rosenthal

Likelihood computations without Bartlett identities; Authors: Per Aslak Mykland

Analysis of change-point estimators under the null hypothesis; Authors: Dietmar Ferger

Minimax hypothesis testing about the density support; Authors: Ghislaine Gayraud

Optimal harvesting from interacting populations in a stochastic environment; Authors: Edward Lungu, Bernt øksendal

Mixed shock models; Authors: Allan Gut

A new fluctuation identity for Lévy processes and some applications; Authors: Larbi Alili, Loïc Chaumont

Editorial board, Bernoulli Journal, vol. 7, no. 3 (2001)

Willem R. van Zwet, Editor-in-Chief

Sara A. van de Geer, Co-Editor

Peter J. Bickel, Editor

D.R. Cox, Editor

David Nualart, Editor

Edward C. Waymire, Editor

Adrian Baddeley, Associate Editor

Lucien Birgé, Associate Editor

Phillipe Carmona, Associate Editor

Paul Embrechts, Associate Editor

Evarist Giné, Associate Editor

Friedrich Götze, Associate Editor

Peter Guttorp, Associate Editor

Frank den Hollander, Associate Editor

Iain Johnstone, Associate Editor

Wilfrid S. Kendall, Associate Editor

M.R. Leadbetter, Associate Editor

Enno Mammen, Associate Editor

Peter McCullagh, Associate Editor

Thomas Mikosch, Associate Editor

Dominique Picard, Associate Editor

David Siegmund, Associate Editor

Simon Tavaré, Associate Editor

Dag Tjøstheim, Associate Editor

Tineke H. Bakker, Editorial Assistant

Richard Leigh, Copy Editor

Ank Lepping, Desk Editor

Ole E. Barndorff-Nielsen (1995-2000), Past Editor-in-Chief

Jens L. Jensen (1995-2000), Past Managing Co-editor

In this paper, we consider the consistency and asymptotic normality of the maximum likelihood estimator for a possibly non-stationary hidden Markov model where the hidden state space is a separable and compact space not necessarily finite, and both the transition kernel of the hidden chain and the conditional distribution of the observations depend on a parameter θ. For identifiable models, consistency and asymptotic normality of the maximum likelihood estimator are shown to follow from exponential memorylessness properties of the state prediction filter and geometric ergodicity of suitably extended Markov chains.

The kriging procedure gives an optimal linear predictor of a spatial process at a point x₀, given observations of the process at other locations x₁,...,x_n, taking into account the spatial dependence of the observations. The kriging predictor is optimal if the weights are calculated from the correct underlying covariance structure. In practice, this covariance structure is unknown and is estimated from the data. An important, but not very well understood, problem in kriging theory is the effect on the accuracy of the kriging predictor of substituting the optimal weights by weights derived from the estimated covariance structure. We show that the effect of estimation is negligible asymptotically if the joint Gaussian distributions of the process at x₀,...,x_n under the true and the estimated covariance are contiguous almost surely. We consider a number of commonly used parametric covariance models where this can indeed be achieved.

We discuss several applications, to large deviations for smooth functions of Gaussian random vectors, of a covariance representation in Gauss space. The existence of this type of representation characterizes Gaussian measures. New representations for Bernoulli measures are also derived, recovering some known inequalities.

This paper introduces a way of constructing non-informative priors for Bayesian analysis, by taking a limit of priors arising from hierarchical constructions as the number of levels in the hierarchy converges to infinity. Results are proved showing that for location families, and other related cases, limits are often not dependent on the exact form of the increment distribution used.

The signed square root statistic R is given by sgn( \hatθ- θ) ( l( \hatθ) - l( θ) )^1/2, where l is the log-likelihood and \hatθ is the maximum likelihood estimator. The pth cumulant of R is typically of the form n^-{p/2}k_p + O(n^-{p+2)/2) , where n is the number of observations. This paper shows how to symbolically compute k_p without invoking the Bartlett identities. As an application, we show how the family of alternatives influences the coverage accuracy of R.

We consider estimators for the change-point in a sequence of independent observations. These are defined as the maximizing points of weighted U-statistic type processes. Our investigations focus on the behaviour of the estimators in the case of independent and identically distributed random variables (null hypothesis of no change), but contiguous alternatives in the sense of Oosterhoff and van Zwet are also taken into account. If the weight functions belong to the Chibisov-O'Reilly class we derive convergence in distribution, including a special Berry-Esseen result. The limit variable is the almost sure unique maximizing point of a weighted (standard or reflected) Brownian bridge with drift. For general weight functions the limiting null distribution is analytically not known. However, in the special case where no weight functions are involved it is known that the maximizer of a standard Brownian bridge is uniformly distributed on the unit interval. A corresponding result for the reflected Brownian bridge seems to be unknown in the literature. In this paper we fill this gap and actually compute the common density of the maximum and its location for a reflected Brownian bridge. From this one can find the density of the maximizer, which analytically can be expressed in terms of a series. In a special case even the finite sample size distribution of our estimator is established. Besides distributional results, we also determine the almost sure set of cluster points.

This paper is concerned with testing nonparametric hypotheses about the underlying support G of independent and identically distributed observations. It is assumed that G belongs to a class {\cal G} of compact sets with smooth upper surface called boundary fragments. It is required to distinguish the simple null hypothesis specified by a known set G₀ in {\cal G} against nonparametric alternatives that G belongs to a class obtained by removing a certain neighbourhood of G₀ in {\cal G}. Using the asymptotical minimax approach, the problem is to determine the order of the smallest distance between the null hypothesis H₀ and the alternatives for which one is able to test the null hypothesis against the alternatives with a given summarized error.

Consider n populations whose sizes are given by stochastic differential equations driven by m-dimensional Brownian motion. We study the following problem: what harvesting strategy from the n populations maximizes the expected total income from the harvest? We formulate this as a (singular) stochastic control problem and give sufficient conditions for the existence of an optimal strategy. Our results lead to the one-at-a-time principle that it is almost surely never optimal to harvest from more than one population at a time.

Traditionally, shock models are of two kinds. The failure (of a system) is related either to the cumulative effect of a (large) number of shocks or it is caused by a shock which is larger than some critical level. The present paper is devoted to a mixed model, in which the system is supposed to break down either because of one (very) large shock, or as a result of many smaller ones.

Let τ and H be respectively the ladder time and ladder height processes associated with a given Lévy process X. We give an identity in law between (τ,H) and (X,H^*), H^* being the right-continuous inverse of the process H. This allows us to obtain a relationship between the entrance law of X and the entrance law of the excursion measure away from 0 of the reflected process (X_t- inf_s≤tX_s, t ≥0). In the stable case, some explicit calculations are provided. These results also lead to an explicit form of the entrance law of the Lévy process conditioned to stay positive.