Table of contents, Bernoulli Journal, vol. 7, no. 1 (2001)

A semi-parametric model for censored and passively registered data; Authors: Marianne A. Jonker, Aad W. Van Der Vaart

Sample splitting with Markov chains; Authors: Anton Schick

On the problem of local adaptive estimation in tomography; Authors: Laurent Cavalier

Generalized Neyman-Pearson lemma via convex duality; Authors: Jaksa Cvitanic, Ioannis Karatzas

On the second-order characteristics of marked point processes; Authors: Martin Schlather

A mixture of the exclusion process and the voter model; Authors: Vladimir Belitsky, Pablo A Ferrari, Mikhail V. Menshikov, Serguei YU. Popov

On stochastic reaction-diffusion equations with singular force term; Authors: Aureli Alabert, István Gyöngy

Support theorem for the solution of a white-noise-driven parabolic stochastic partial differential equation with temporal Poissonian jumps; Authors: Nicolas Fournier

Editorial board, Bernoulli Journal, vol. 7, no. 1 (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

We consider the estimation of the parameters in a semi-parametric model for life-history data from historical demography. The data consist of a sequence of times of life events that is either ended by a time of death or right-censored by an unobserved time of migration. We derive the properties of the maximum likelihood estimators of the parameters and prove their asymptotic efficiency. Estimating the migration distribution turns out to be an inverse problem, whereas the other parameters are regular. The proof is based on a uniform rate of convergence of the Grenander estimator of a monotone density and bounds on the number and spacings of its support points.

Sample splitting techniques play an important role in constructing estimates with prescribed influence functions in semi-parametric and nonparametric models when the observations are independent and identically distributed. This paper shows how a contiguity result can be used to modify these techniques to the case when the observations come from a stationary and ergodic Markov chain. As a consequence, sufficient conditions for the construction of efficient estimates in semi-parametric Markov chain models are obtained. The applicability of the resulting theory is demonstrated by constructing an estimate of the innovation variance in a nonparametric autoregression model, by constructing a weighted least-squares estimate with estimated weights in an autoregressive model with martingale innovations, and by constructing an efficient and adaptive estimate of the autoregression parameter in a heteroscedastic autoregressive model with symmetric errors.

The principle of tomography is to reconstruct a multidimensional function from observations of its integrals over hyperplanes. We consider here a model of stochastic tomography where we observe the Radon transform Rf of the function f with a stochastic error. Then we construct a `data-driven' estimator which does not depend on any a priori smoothness assumptions on the function f. Considering pointwise mean-squared error, we prove that it has (up to a log) the same asymptotic properties as an oracle. We give an example of Sobolev classes of functions where our estimator converges to f(x) with the optimal rate of convergence up to a log factor.

We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach, first employed by Witting. Results of Aubin and Ekeland from non-smooth convex analysis are used, along with a theorem of Komlós, in order to establish the existence of a max-min optimal test in considerable generality, and to investigate its properties. The theory is illustrated on representative examples involving Gaussian measures on Euclidean and Wiener space.

New definitions for the second-order characteristics of marked point processes are presented. Non-reduced moment measures are involved in obtaining consistency with ana\-logous definitions in the random field context. A certain σ-algebra replaces the current assumptions on stationarity and isotropy so that the characteristics are still well defined even if such assumptions do not hold. The new definitions and the present ones coincide for positive arguments if the marked point process is simple, stationary and isotropic, and if the second-order product density exists. The different second-order characteristics given in the literature are discussed. A renaming of one of the characteristics is suggested since distinct characteristics have been known under identical names. Furthermore, it is shown that arbitrary measurable functions with compact support can appear as second-order characteristics of marked point processes.

We consider a one-dimensional nearest-neighbour interacting particle system, which is a mixture of the simple exclusion process and the voter model. The state space is taken to be the countable set of the configurations that have a finite number of particles to the right of the origin and a finite number of empty sites to the left of it. We obtain criteria for the ergodicity and some other properties of this system using the method of Lyapunov functions.

We prove an existence and uniqueness theorem for stochastic reaction-diffusion equations driven by space-time white noise in one spatial dimension, when the diffusion coefficient is non-degenerate and the force term is only measurable and can be locally unbounded.

We study the weak solution X of a parabolic stochastic partial differential equation driven by two independent processes: a Gaussian white noise and a finite Poisson measure. We characterize the support of the law of X as the closure in \mathbb{D}≤ft( [0,T], \mathbb{C}([0,1])\right), endowed with its Skorokhod topology, of a set of weak solutions of ordinary partial differential equations.