Table of contents, Bernoulli Journal, vol. 10, no. 5 (2004)

Transportation of measure, Young diagrams and random matrices; Authors: Gordon Blower

Solutions of stochastic partial differential equations considered as Dirichlet processes; Authors: Denis Laurent

Large deviations for global maxima of independent superadditive processes with negative drift and an application to optimal sequence alignments; Authors: Steffen Grossmann, Benjamin Yakir

Weak convergence of empirical copula processes; Authors: Jean-David Fermanian, Dragan Radulovic, Marten Wegkamp

Dutch book against some `objective' priors; Authors: Morris L. Eaton, David A. Freedman

Asymptotically exact minimax estimation in sup-norm for anisotropic Hölder classes; Authors: Karine Bertin

Functional convergence and optimality of plug-in estimators for stationary densities of moving average processes; Authors: Anton Schick, Wolfgang Wefelmeyer

Nonparametric methods of inference for finite-state, inhomogeneous Markov processes; Authors: Peter Hall, Efstathia Bura

Editorial board, Bernoulli Journal, vol. 10, no. 5 (2004)

Peter McCullagh, Editor-in-Chief

Peter J. Bickel, Editor

D.R. Cox, Editor

David Nualart, Editor

Edward Waymire, Editor

Lucien Birgé, Associate Editor

Evarist Giné, Associate Editor

Peter Hall, Associate Editor

Wilfrid S. Kendall, Associate Editor

Xiao-Li Meng, Associate Editor

Thomas Mikosch, Associate Editor

Dominique Picard, Associate Editor

Yaacov Ritov, Associate Editor

David Siegmund, Associate Editor

Dag Tjøstheim, Associate Editor

Sara van de Geer, Associate Editor

Alan Welsh, Associate Editor

Mitzi Nakatsuka, Editorial Assistant

Richard Leigh, Copy Editor

Ank Lepping, Desk Editor

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

Willem R. van Zwet, Past Editors-in-Chief(2000-2003)

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

Sara van de Geer, Past Co-Editors (2000-2003)

The theory of transportation of measure for general convex cost functions is used to obtain a novel logarithmic Sobolev inequality for measures on phase spaces of high dimension and hence a concentration-of-measure inequality. There are applications to the Plancherel measure associated with the symmetric group, the distribution of Young diagrams partitioning N as N→∞ and to the mean-field theory of random matrices. For the potential logΓ(x+1), the generalized orthogonal ensemble and its empirical eigenvalue distribution are shown to satisfy a Gaussian concentration-of-measure phenomenon. Hence the empirical eigenvalue distribution converges weakly almost surely as the matrix size increases; the limiting density is given by the derivative of the Vershik probability density.

We consider the parabolic stochastic partial differential equation $$u(t,x)=\Phi \left(x\right)+{\int }_0^t\mathrm{Lu}(s,x)+f(s,x,u(s,x),\mathrm{Du}(s,x\left)\right)ds$$ $$+{\int }_0^t{g}_i(s,x,u(s,x),\mathrm{Du}(s,x\left)\right)d{B}_s^i,$$ \noindent where f and g are supposed to be Lipschitzian and L is a self-adjoint operator associated with a Dirichlet form defined on a finite- or infinite-dimensional space. We prove that it admits a unique solution which is a Dirichlet process and, thanks to Itô's formula for Dirichlet processes, we prove a comparison theorem.

We examine the distribution of the global maximum of an independent superadditive process with negative drift. We show that, under certain conditions, the distribution's upper tail decays exponentially at a rate that can be characterized as the unique positive zero of some limiting ogarithmic moment generating functio. This result extends the corresponding one for random walks with a negative drift. We apply our results to sequence alignments with gaps. Calculating p-values of optimal gapped alignment scores is still one of the most challenging mathematical problems in bioinformatics. Our results provide a better understanding of the tail of the optimal score's distribution, especially at the level of large deviations, and they are in accord with common practice of statistical evaluation of optimal alignment results. However, a complete mathematical description of the optimal score's distribution remains far from reach.

Weak convergence of the empirical copula process has been established by Deheuvels in the case of independent marginal distributions. Van der Vaart and Wellner utilize the functional delta method to show convergence in ${\ell }^{\mathrm{\infty }}\left(\right[a,b{]}^2)$ for some 0<a<b<1, under restrictions on the distribution functions. We extend their results by proving the weak convergence of this process in ${\ell }^{\mathrm{\infty }}\left(\right[0,1{]}^2)$ under minimal conditions on the copula function, which coincides with the result obtained by Gaenssler and Stute. It is argued that the condition on the copula function is necessary. The proof uses the functional delta method and, as a consequence, the convergence of the bootstrap counterpart of the empirical copula process follows immediately. In addition, weak convergence of the smoothed empirical copula process is established.

`Dutch book' and `strong inconsistency' are generally equivalent: there is a system of bets that makes money for the gambler, whatever the state of nature may be. As de Finetti showed, an odds-maker who is not a Bayesian is subject to a Dutch book, under certain highly stylized rules of play - a fact often used as an argument against frequentists. However, so-called `objective' or `uninformative' priors may also be subject to a Dutch book. This note explains, in a relatively simple and self-contained way, how to make Dutch book against a frequently recommended uninformative prior for covariance matrices.

We consider the Gaussian white noise model and study the estimation of a function f in the uniform norm assuming that f belongs to a Hölder anisotropic class. We give the minimax rate of convergence over this class and determine the minimax exact constant and an asymptotically exact estimator.

We give new results, under mild assumptions, on convergence rates in L₁ and L₂ for residual-based kernel estimators of the innovation density of moving average processes. Exploiting the convolution representation of the stationary density of moving average processes, these estimators can be used to obtain n^1/2-consistent plug-in estimators for this stationary density. Here we derive functional weak convergence results in L₁ and C₀(R) for these plug-in estimators. If efficient estimators for the finite-dimensional parameters of the process are used in our construction, semiparametric efficiency of our plug-in estimators is obtained.

In some inferential problems involving Markov process data, the inhomogeneity of the process is of central interest. One example is of a binary time series of data on the presence or absence of a species at a particular site over time. Here the two states correspond to `presence' or `absence', respectively, of the species, and the main topic of interest is temporal variation in the process. In principle this variation can be modelled parametrically, but in the absence of information about the physical mechanism causing species numbers to fluctuate, it is usually very difficult to suggest a plausible model that explains the data, at least until a more adaptive analysis is conducted. These issues argue in favour of nonparametric methods for estimating probabilities of transition, and for estimating probabilities of the process being in a given state at a given time. Such techniques, which in practice might be a prelude to parametric modelling, will be introduced and explored, under assumptions motivated by characteristics of the data set mentioned above. These assumptions will be shown to lead to consistent estimation of probabilities, and so to imply that nonparametric methodology gives accurate information about properties of the process.