Table of contents, Bernoulli Journal, vol. 4, no. 4 (1998)

Consistency of Bayes estimates for nonparametric regression: normal theory; Authors: Persi W. Diaconis, David Freedman

Quasilinear stochastic elliptic equations with reflection: the existence of a density; Authors: Samy Tindel

Upper functions for plane Brownian windings; Authors: Eugene A. Dorofeev

On association models defined over independence graphs; Authors: Nanny Wermuth, David R. Cox

Approximate distributions for the various serial correlograms; Authors: Ronald W. Butler, Marc S. Paolella

Efficient estimation of analytic density under random censorship; Authors: Eduard Belitser

Editorial board, Bernoulli Journal, vol. 4, no. 4 (1998)

Ole E. Barndorff-Nielsen, Editor-in-Chief

Jens Ledet Jensen, Managing Co-Editor

Peter J. Bickel, Editor

David Nualart, Editor

David R. Cox, Editor

Edward C. Waymire, Editor

Adrian Baddeley, Associate Editor

Lucien Birgé, Associate Editor

Louis H. Y. Chen, Associate Editor

Hans Föllmer, Associate Editor

Richard D. Gill, Associate Editor

Peter Guttorp, Associate Editor

Peter McCullagh, Associate Editor

Alexander A. Novikov, Associate Editor

Yosihiko Ogata, Associate Editor

Victor Pérez-Abreu, Associate Editor

Terence P. Speed, Associate Editor

Dag Tjøstheim, Associate Editor

Ank Lepping, Desk Editor

Performance characteristics of Bayes estimates are studied. More exactly, for each subject in a data set, let ξ be a vector of binary covariates and let Y be a normal response variable, with E{Y|ξ}=f(ξ) and var{Y|ξ}=1. Here, f is an unknown function to be estimated from the data; the subjects are independent and identically distributed. Define a prior distribution on f as ∑_kw_kπ_k/∑_kw_k, where π_k is standard normal on the set of f which only depend on the first k covariates and w_k>0 for infinitely many k. Bayes estimates are consistent for all f. On the other hand, if the π_k are flat, inconsistency is the rule.

In this paper we prove the absolute continuity of the law of the solution to an elliptic stochastic partial differential equation with an additive white noise reflected at zero. The proof is based on Malliavin's calculus tools, and some methods of variational inequalities and ordinary partial differential equations driven by measure data.

We present a method leading to a number of results on upper functions for such functionals as winding angles or radius vectors of planar processes.

Conditions on joint distributions are given under which two variables will be conditionally associated whenever an independence graph does not imply a corresponding conditional independence statement. To this end the notions of parametric cancellation, of stable paths and of quasi-linear models are discussed in some detail.

Saddlepoint methods are used to approximate the joint density of the serial correlogram up to lag m. Jacobian transformations also lead to approximations for the related partial correlogram and inverse correlogram. The approximations consider non-circularly and circularly defined models in both the null and the non-null settings. The distribution theory encompasses the standard non-circularly defined correlogram computed from least-squares residuals removing arbitrary fixed regressors. Connections of the general theory to the approximations given by Daniels and by Durbin in the circular setting are indicated. The double-saddlepoint density and distribution approximations are given for the conditional distribution of the non-circular lag m serial correlation given the previous lags from order 1 to m-1. This allows for the computation of p values in conditional inference when testing that the model is AR(m-1) versus AR(m). Numerical comparisons with the tests of Daniels and of Durbin suggest that their tests based on circularity assumptions are inadequate for short non-circular series but are in close agreement with the non-circular tests for moderately long series.

The nonparametric minimax estimation of an analytic density at a given point, under random censorship, is considered. Although the problem of estimating density is known to be irregular in a certain sense, we make some connections relating this problem to the problem of estimating smooth functionals. Under condition that the censoring is not too severe, we establish the exact limiting behaviour of the local minimax risk and propose the efficient (locally asymptotically minimax) estimator - an integral of some kernel with respect to the Kaplan-Meier estimator.

Acknowledgement of refereeing work BJ vol. 04

Annual index BJ vol. 04

Keyword index BJ vol. 04