Table of contents, Bernoulli Journal, vol. 5, no. 4 (1999)

An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions; Authors: Ilkka Norros, Esko Valkeila, Jorma Virtamo

Scale-invariant diffusions: transience and non-polar points; Authors: Richard Dante Deblassie

On the convergence of Dirichlet processes; Authors: François Coquet, Leszek Słomiński

Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes; Authors: Olle Häggström,, Marie-Colette N.M. Van Lieshout, Jesper Møller

Regression rank-scores tests against heavy-tailed alternatives; Authors: Jana Jureckova

Self-similarity of mathematical likelihood; Authors: Stephen Raymond Chamberlin

On multivariate median regression; Authors: Biman Chakraborty

Likelihood ratio tests in contamination models; Authors: Mohamed Lemdani, Odile Pons

The exponential statistical manifold: mean parameters, orthogonality and space transformations; Authors: Giovanni Pistone, Maria Piera Rogantin

Editorial board, Bernoulli Journal, vol. 5, no. 4 (1999)

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

Søren Asmussen, Associate Editor

Adrian Baddeley, Associate Editor

Lucien Birgé, Associate Editor

Philippe Carmona, Associate Editor

Louis H. Y. Chen, Associate Editor

Hans Föllmer, Associate Editor

Valentine Genon-Catalot, 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

Andrea Rotnitzky, Associate Editor

Terence P. Speed, Associate Editor

Dag Tjøstheim, Associate Editor

Richard L. Tweedie, Associate Editor

Andrew T.A. Wood, Associate Editor

Ank Lepping, Desk Editor

The Radon-Nikodym derivative between a centred fractional Brownian motion Z and the same process with constant drift is derived by finding an integral transformation which changes Z to a process with independent increments. A representation of Z through a standard Brownian motion on a finite interval is given. The maximum-likelihood estimator of the drift and some other applications are presented.

Consider a diffusion in R^d (d ≥2) whose generator has coefficients independent of the distance to the origin. Then there is a parameter α so that the origin is almost surely hit when α< 1 and almost surely not hit when α> 1. Moreover, the process is transient to ∞ for α> 1. We identify α in terms of the diffusion coefficients and a certain invariant measure. In some special two-dimensional cases we explicitly compute the invariant measure and resolve the critical case α= 1. This work complements and extends certain results of Pinsky (1995) and Williams (1985).

For a given weakly convergent sequence {Xⁿ} of Dirichlet processes we show weak convergence of the sequence of the corresponding quadratic variation processes as well as stochastic integrals driven by the Xⁿ values provided that the condition UTD (a counterpart to the condition UT for Dirichlet processes) holds true. Moreover, we show that under UTD the limit process of {Xⁿ} is a Dirichlet process, too.

The area-interaction process and the continuum random-cluster model are characterized in terms of certain functional forms of their respective conditional intensities. In certain cases, these two point process models can be derived from a bivariate point process model which in many respects is simpler to analyse and simulate. Using this correspondence we devise a two-component Gibbs sampler, which can be used for fast and exact simulation by extending the recent ideas of Propp and Wilson. We further introduce a Swendsen-Wang type algorithm. The relevance of the results within spatial statistics as well as statistical physics is discussed.

Statistical inference in the linear model based on the concept of regression rank scores is invariant to the nuisance regression; hence regression rank-scores tests need no estimation of the nuisance parameters. Such tests, already available in the literature, are manageable, asymptotically distribution-free and have many convenient properties, but they are either censored or applicable only to light-tailed distributions. To extend the universality of regression rank-scores tests, we propose modified tests applicable to heavy-tailed distributions including Cauchy. Depending on the alternative we want to treat by the test, we censor the score generating function but the censoring is asymptotically negligible. The proposed tests, being asymptotically distribution-free, are as efficient as the ordinary rank tests without nuisance parameters, for a broad class of density shapes.

We study sufficiency in terms of the extent to which the Taylor series expansion of the normed log-likelihood function generated by the sampling distribution of a statistic conforms to that of the sample normed log-likelihood function, and give an associated self-similar property of mathematical likelihood (not self-similarity in the sense of self-similar stochastic processes).

An extension of the concept of least absolute deviation regression for problems with multivariate response is considered. The approach is based on a transformation and retransformation technique that chooses a data-driven coordinate system for transforming the response vectors and then retransforms the estimate of the matrix of regression parameters, which is obtained by performing coordinatewise least absolute deviations regression on the transformed response vectors. It is shown that the estimates are equivariant under non-singular linear transformations of the response vectors. An algorithm called TREMMER (Transformation Retransformation Estimates in Multivariate MEdian Regression) has been suggested, which adaptively chooses the optimal data-driven coordinate system and then computes the regression estimates. We have also indicated how resampling techniques like the bootstrap can be used to conveniently estimate the standard errors of TREMMER estimates. It is shown that the proposed estimate is more efficient than the non-equivariant coordinatewise least absolute deviations estimate, and it outperforms ordinary least-squares estimates in the case of heavy-tailed non-normal multivariate error distributions. Asymptotic normality and some other optimality properties of the estimate are also discussed. Some interesting examples are presented to motivate the need for affine equivariant estimation in multivariate median regression and to demonstrate the performance of the proposed methodology.

We study the asymptotic distribution of the likelihood ratio statistic to test whether the contamination of a known density f₀ by another density of the same parametric family reduces to f₀. The classical asymptotic theory for the likelihood ratio statistic fails, and we propose a general reparametrization which ensures regularity properties. Under the null hypothesis, the likelihood ratio statistic converges to the supremum of a squared truncated Gaussian process. The result is extended to the case of the contamination of a mixture of p known densities by q other densities of the same family.

Let $(X,calX,\mu )$ be a measure space, and let $calM(X,calX,\mu )$ denote the set of the $\mu$-almost surely strictly positive probability densities. It was shown by Pistone and Sempi in 1995 that the global geometry on $calM(X,calX,\mu )$ can be realized by an affine atlas whose charts are defined locally by the mappings $calM(X,calX,\mu )\supset {calU}_p\ni q\mapsto log(q/p)+K(p,q)\in B_p$, where ${calU}_p$ is a suitable open set containing $p$, $K(p,q)$ is the Kullback--Leibler relative information and $B_p$ is the vector space of centred and exponentially $(p\cdot \mu )$-integrable random variables. In the present paper we study the transformation of such an atlas and the related manifold structure under basic transformations, i.e. measurable transformation of the sample space. A generalization of the mixed parametrization method for exponential models is also presented.