Table of contents, Bernoulli Journal, vol. 10, no. 2 (2004)

On minimax density estimation on \mathbb{R}}; Authors: Anatoli Juditsky, Sophie Lambert-Lacroix

Berry-Esseen and central limit theorems for serial rank statistics via graphs; Authors: Tatyana S. Turova

Bivariate tail estimation: dependence in asymptotic independence; Authors: Gerrit Draisma, Holger Drees, Ana Ferreira, Laurens De Haan

Transition density estimation for stochastic differential equations via forward-reverse representations; Authors: Grigori N. Milstein, John G.M. Schoenmakers, Vladimir Spokoiny

Martingale-type stochastic calculus for anticipating integral processes; Authors: Ciprian A. Tudor

Stable limits of sums of bounded functions of long-memory moving averages with finite variance; Authors: Donatas Surgailis

On roughness indices for fractional fields; Authors: Albert Benassi, Serge Cohen, Jacques Istas

Editorial board, Bernoulli Journal, vol. 10, no. 2 (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 problem of density estimation on \mathbb{R}} on the basis of an independent sample X₁,..., X_N with common density f is discussed. The behaviour of the minimax L_p risk, 1≤p≤∞, is studied when f belongs to a Hölder class of regularity s on the real line. The lower bound for the minimax risk is given. We show that the linear estimator is not efficient in this setting and construct a wavelet adaptive estimator which attains (up to a logarithmic factor in N) the lower bounds involved. We show that the minimax risk depends on the parameter p when p<2+ 1/s.

We use Stein's method in combination with notions from graph theory to obtain Berry-Esseen and central limit theorems for generalized serial rank statistics.

In the classical setting of bivariate extreme value theory, the procedures for estimating the probability of an extreme event are not applicable if the componentwise maxima of the observations are asymptotically independent. To cope with this problem, Ledford and Tawn proposed a submodel in which the penultimate dependence is characterized by an additional parameter. We discuss the asymptotic properties of two estimators for this parameter in an extended model. Moreover, we develop an estimator for the probability of an extreme event that works in the case of asymptotic independence as well as in the case of asymptotic dependence, and prove its consistency.

The general reverse diffusion equations are derived and applied to the problem of transition density estimation of diffusion processes between two fixed states. For this problem we propose density estimation based on forward-reverse representations and show that this method allows essentially better results to be achieved than the usual kernel or projection estimation based on forward representations only.

We prove that the class of Skorohod integral processes coincides with a class of Itôintegrals. Using the techniques of the classical Itôstochastic calculus, we develop a new stochastic calculus for Skorohod integral processes, different from that introduced by Nualart and Pardoux.

We discuss limit distributions of partial sums of bounded functions h of a long-memory moving-average process X_t= ∑_j=1 ^∞ b_j ζ_t-j with coefficients b_j decaying as j^-β, 1/2< β< 1, and independent and identically distributed innovations ζ_s whose probability tails decay as x^-α, 2< α< 4. The case of h having Appell rank k_*=2 or 3 is discussed in detail. We show that in this case and in the parameter region αβ< 2 , the partial sums process, normalized by N^1/αβ , weakly converges to an αβ-stable Lévy process, provided that the normalization dominates the corresponding k_* th-order Hermite process normalization, or that 1/αβ> 1 - (2β-1)k_*/2. A complete characterization of limit distributions of the partial sums process remains open.

The class of moving-average fractional Lévy motions (MAFLMs), which are fields parameterized by a d-dimensional space, is introduced. MAFLMs are defined by a moving-average fractional integration of order H of a random Lévy measure with finite moments. MAFLMs are centred d-dimensional motions with stationary increments, and have the same covariance function as fractional Brownian motions. They have H-d/2 Hölder-continuous sample paths. When the Lévy measure is the truncated random stable measure of index α, MAFLMs are locally self-similar with index \widetilde{H} =H -d/2+d/ α. This shows that in a non-Gaussian setting these indices (local self-similarity, variance of the increments, Hölder continuity) may be different. Moreover, we can establish a multiscale behaviour of some of these fields. All the indices of such MAFLMs are identified for the truncated random stable measure.