Table of contents, Bernoulli Journal, vol. 12, no. 2 (2006)

Asymptotic error rates in third-generation wireless systems; Authors: Marten J. Klok

Selecting models with different spectral density matrix structures by the cross-validated log likelihood criterion; Authors: Yasumasa Matsuda, Yoshihiro Yajima, Howell Tong

Hypothesis testing for families of ergodic processes; Authors: Andrew B. Nobel

Optimal estimation in additive regression models; Authors: Joel Horowitz,, Jussi Klemelä, Enno Mammen

Empirical likelihood in some semiparametric models; Authors: Patrice Bertail

An exponential inequality under weak dependence; Authors: Raoul S. Kallabis, Michael H. Neumann

Adaptive density estimation using the blockwise Stein method; Authors: Philippe Rigollet

A characterization of Poisson-Gaussian families by generalized variance; Authors: Célestin C. Kokonendji, Afif Masmoudi

Erratum: Identification of multifractional Brownian motion; Authors: Jean-François Coeurjolly

Editorial board, Bernoulli Journal, vol. 12, no. 2 (2006)

Peter McCullagh, Editor-in-Chief

Peter J. Bickel, Editor

D.R. Cox, Editor

David Nualart, Editor

Edward Waymire, Editor

David Applebaum, Associate Editor

Lucien Birgé, Associate Editor

Evarist Giné, Associate Editor

Peter Hall, Associate Editor

Wilfrid S. Kendall, Associate Editor

Thomas Mikosch, Associate Editor

Jesper Møller, Associate Editor

Gesine Reinert, Associate Editor

Ya'acov Ritov, Associate Editor

David Siegmund, Associate Editor

Dag Tjøstheim, Associate Editor

Alexandre Tsybakov, Associate Editor

Sara van de Geer, Associate Editor

Eva Bjorn Vedel Jensen, Associate Editor

Alan Welsh, Associate Editor

Wei-Biao Wu, 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 introduction of the so-called third-generation wireless communication system, also known as UMTS or IMT-2000, is a large-scale revolution in telecommunications. It uses a technique called code division multiple access (CDMA). An advanced algorithm to improve the performance of such a CDMA system is called hard-decision parallel interference cancellation and was studied by van der Hofstad and Klok for a rather basic model. We extend many of their results to a more realistic model, where different users transmit at different powers and where additive noise is present.

We propose the cross-validated log likelihood (CVLL) criterion for selecting multivariate time series models with different forms of the spectral density matrix, which correspond to different constraints on the component time series such as mutual independence, separable correlation, time reversibility, graphical interaction and others. We obtain asymptotic properties of the CVLL, and demonstrate the empirical properties of the CVLL selection with both simulated and real data.

General sufficient conditions for the discernibility of two families of stationary ergodic processes are derived. The conditions involve the weak topology for stationary processes. They are analogous in several respects to existing conditions for the discernibility of families of independent and identically distributed (i.i.d.) processes, but require a more refined type of topological separation in the general case. As a first application of the conditions, it is shown how existing discernibility results for i.i.d. processes may be extended to a countable union of uniformly ergodic families. In addition, it is shown how one may use hypothesis testing to study polynomial decay rates for covariance-based mixing conditions.

This paper is concerned with optimal estimation of the additive components of a nonparametric, additive regression model. Several different smoothing methods are considered, including kernels, local polynomials, smoothing splines and orthogonal series. It is shown that, asymptotically up to first order, each additive component can be estimated as well as it could be if the other components were known. This result is used to show that in additive models the asymptotically optimal minimax rates and constants are the same as they are in nonparametric regression models with one component.

We study the properties of empirical likelihood for Hadamard differentiable functionals tangentially to a well chosen set and give some extensions in more general semiparametric models. We give a straightforward proof of its asymptotic validity and Bartlett correctability, essentially based on two ingredients: convex duality and local asymptotic normality properties of the empirical likelihood ratio in its dual form. Extensions to semiparametric problems with estimated infinite-dimensional parameters are also considered. We give some applications to confidence intervals for the location parameter of a symmetric model, M-estimators with some nuisance parameters and general functionals in biased sampling models.

Doukhan and Louhichi introduced a covariance-based concept of weak dependence which is more general than classical mixing concepts. We prove a Bernstein-type inequality under this condition which is similar to the well-known inequality in the independent case. We apply this tool to derive asymptotic properties of penalized least-squares estimators in Barron's classes.

We study the problem of nonparametric estimation of a probability density of unknown smoothness in L₂(R). Expressing mean integrated squared error (MISE) in the Fourier domain, we show that it is close to mean squared error in the Gaussian sequence model. Then applying a modified version of Stein's blockwise method, we obtain a linear monotone oracle inequality. Two consequences of this oracle inequality are that the proposed estimator is sharp minimax adaptive over a scale of Sobolev classes of densities, and that its MISE is asymptotically smaller than or equal to that of kernel density estimators with any bandwidth provided that the kernel belongs to a large class of functions including many standard kernels.

We show that if the generalized variance of an infinitely divisible natural exponential family $F=F\left(\mu \right)$ in a $d$ -dimensional linear space is of the form $det{K}_{\mu }^{\text{'}\text{'}}\left(\theta \right)=exp({\theta }^{T}b+c)$, then there exists $k$ in $\{0,1,...,d\}$ such that $F$ is a product of $k$ univariate Poisson and ($d-k$)-variate Gaussian families. In proving this fact, we use a suitable representation of the generalized variance as a Laplace transform and the result, due to Jörgens, Calabi and Pogorelov, that any strictly convex smooth function $f$ defined on the whole of $R^d$ such that $det{f}^{\text{'}\text{'}}\left(\theta \right)$ is a positive constant must be a quadratic form.

An error has been found in the expression given in the proof of Lemma 2 at the top of p. 1001. See Bernoulli Journal 11, December 2005.