Table of contents, International Statistical Review, vol. 72, no. 3 (2004)

Causality: a Statistical View; Authors: D.R. Cox, Nanny Wermuth

A Foundational Justification for a Weighted Likelihood Approach to Inference; Authors: Russell J. Bowater

Comments on ``A Foundational Justification for a Weighted Likelihood Approach to Inference''; Authors: Glenn Shafer

Rejoinder; Authors: Russell J. Bowater

Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey; Authors: Helle Sørensen

A Coincident Index for the State of the Economy; Authors: Fabio H. Nieto

Recent Developments of Statistical Approaches in Aspects of Accounting:\\ a Review; Authors: Michael Falta, Rodney Wolff

A Comparative Analysis of Different IV and GMM Estimators of Dynamic Panel Data Models; Authors: Mark N. Harris, László Mátyás

Statistical Inference under Symmetry; Authors: Inge S. Helland

Editorial board, International Statistical Review, vol. 72, no. 3 (2004)

E. Seneta (School Math. & Statist., Univ. Sydney, Australia) Joint Editor

A.M. Manninen (City of Helsinki, Urban Facts, Finland) Joint Editor

Ann Daniels (ISI, Voorburg, The Netherlands) Executive Editor

R. Acx (National Bank of Belgium, Brussels) Associate Editor

T. Alanko (Statistics Finland) Associate Editor

D. Balding (Imperial Coll. Fac.Med., London, UK) Associate Editor

R. Gill (Univ. Utrecht, The Netherlands) Associate Editor

P. Guttorp (Univ. Washington, Seattle, USA) Associate Editor

W. Lutz (Internat. Inst. Appl. Systems Analysis, Laxenburg, Austria) Associate Editor

N. Singpurwalla (George Washington Univ.,Washington, USA) Associate Editor

I. Stamhuis (Free Univ., Amsterdam, The Netherlands) Associate Editor

P. Verdier (INSEE, Paris, France) Associate Editor

N. Weber (School Math. and Statist., Univ. Sydney, Australia) Associate Editor

E. Wegman (George Mason Univ., Fairfax, USA) Associate Editor

C. Wild (Univ. Auckland, New Zealand) Associate Editor

Statistical aspects of causality are reviewed in simple form and the impact of recent work discussed. Three distinct notions of causality are set out and implications for densities and for linear dependencies explained. The importance of appreciating the possibility of effect modifiers is stressed, be they intermediate variables, background variables or unobserved confounders. In many contexts the issue of unobserved confounders is salient. The difficulties of interpretation when there are joint effects are discussed and possible modifications of analysis explained. The dangers of uncritical conditioning and marginalization over intermediate response variables are set out and some of the problems of generalizing conclusions to populations and individuals explained. In general terms the importance of search for possibly causal variables is stressed but the need for caution is emphasized.

Two types of probability are discussed, one of which is additive whilst the other is non-additive. Popular theories that attempt to justify the importance of the additivity of probability are then critically reviewed. By making assumptions the two types of probability put forward are utilised to justify a method of inference which involves betting preferences being revised in light of the data. This method of inference can be viewed as a justification for a weighted likelihood approach to inference where the plausibility of different values of a parameter θ based on the data $\tilde{x}$ is measured by the quantity $q\left(\theta \right)=l(\tilde{x},\theta )w\left(\theta \right)$, where $l(\tilde{x},\theta )$ is the likelihood function and w(θ) is a weight function. Even though, unlike Bayesian inference, the method has the disadvantageous property that the measure q(θ) is generally non-additive, it is argued that the method has other properties which may be considered very desirable and which have the potential to imply that when everything is taken into account, the method is a serious alternative to the Bayesian approach in many situations. The methodology that is developed is applied to both a toy example and a real example.

Russell Bowater uses non-additive probability to interpret weighted likelihood. As I have written a great deal about non-additive probability, the editor has asked me to comment.

I welcome the comments that have been made by Professor Shafer. He makes a number of important points, however, I shall confine this rejoinder by addressing only a selected number of these points. In particular, I would like to use this opportunity to briefly comment on how well I feel the work that has been done by those in the `imprecise probabilities' community, tackles the specific shortcomings of the standard Bayesian approach that have been highlighted in my article.

This paper is a survey of estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and so-called simple estimating functions; (ii) analytical and numerical approximations of the likelihood function which can in principle be made arbitrarily accurate; (iii) Bayesian analysis and MCMC methods; and (iv) indirect inference and EMM which both introduce auxiliary (but wrong) models and correct for the implied bias by simulation.

In this paper, a methodology is developed for designing a coincident index for the so-called state of the economy. Based on this index, statistical tests are deduced for checking structural changes in the economy and consistency of pre-established economic goals for the short term with past and present observed information. The approach can also be considered as a new solution for the ex post (benchmarking, disaggregation) and ex ante (extrapolation) prediction problems.

We review and simultaneously introduce a convenient statistical concept for the mathematical representation of the Statistical Activity Cost Theory (SACT) introduced by Willett (1987, 1988). Further, we discuss, and present a critique of a variety of statistical models with respect to long debated accounting problems, such as the allocation of joint costs and depreciation. We finally propose that taking the effort to combine those models results in a novel statistical accounting system and this is discussed by means of the so-called virtual firm. Our approach is methodological rather than empirical. We endeavour to demonstrate that the statistical models presented herein have a more natural interpretation and applicability than their deterministic analogues: hence, this review presents promising outcomes and useful perspectives for the accounting profession.

It is well known that the usual procedures for estimating panel data models are inconsistent in the dynamic setting. A large number of consistent estimators however, have been proposed in the literature. This paper provides a survey of the majority of mainstream estimators, which tend to consist of IV and GMM ones. It also considers a newly proposed extension to the promising Wansbeek-Bekker estimator (Harris & Mátyás, 2000). To provide guidance to the applied researcher working on micro-datasets, the small sample performance of these estimators is evaluated using a set of Monte Carlo experiments.

We explore the consequences of adjoining a symmetry group to a statistical model. Group actions are first induced on the sample space, and then on the parameter space. It is argued that the right invariant measure induced by the group on the parameter space is a natural non-informative prior for the parameters of the model. The permissible sub-parameters are introduced, i.e., the subparameters upon which group actions can be defined. Equivariant estimators are similarly defined. Orbits of the group are defined on the sample space and on the parameter space; in particular the group action is called transitive when there is only one orbit. Credibility sets and confidence sets are shown (under right invariant prior and assuming transitivity on the parameter space) to be equal when defined by permissible sub-parameters and constructed from equivariant estimators. The effect of different choices of transformation group is illustrated by examples, and properties of the orbits on the sample space and on the parameter space are discussed. It is argued that model reduction should be constrained to one or several orbits of the group. Using this and other natural criteria and concepts, among them concepts related to design of experiments under symmetry, leads to links towards chemometrical prediction methods and towards the foundation of quantum theory.

Annual index ISR vol. 72

Acknowledgement of refereeing work