Table of contents, International Statistical Review, vol. 74, no. 2 (2006)

Survey Estimates by Calibration on Complex Auxiliary Information; Authors: Victor M. Estevao, Carl-Erik Särndal

A Measure of Representativeness of a Sample for Inferential Purposes; Authors: Salvatore Bertino

Estimation Optimality of Corrected AIC and Modified Cp in Linear Regression; Authors: Simon L. Davies, Andrew A. Neath, Joseph E. Cavanaugh

Statistical Proofs of Some Matrix Theorems; Authors: C. Radhakrishna Rao

The Trigonometry of Matrix Statistics; Authors: Karl Gustafson

Comparison of Sampling Schemes for Dynamic Linear Models; Authors: Edna A. Reis, Esther Salazar, Dani Gamerman

A Comparison of Nonparametric Methods in the Graduation of Mortality: Application to Data from the Valencia Region (Spain); Authors: Ana Debón, Francisco Montes, Ramón Sala

Stochastic Index Numbers: A Review; Authors: Kenneth W. Clements, Izan H.Y. Izan, E. Antony Selvanathan

Peruco: A Method for Producing Safe and Consistent Microdata; Authors: Leon Willenborg, Ardo van den Hout

Editorial board, International Statistical Review, vol. 74, no. 2 (2006)

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

K. Zeelenberg (Statistics Netherlands, Voorburg), Joint Editor

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

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

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

T. Alanko (Statistics Finland), 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. & Statist., Univ. Sydney, Australia),, Associate Editor

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

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

T.E. Dalenius,, Former Editor

L.A.M. Vessereau,, Former Editor

W.R. Buckland,, Former Editor

O.E. Barndorff-Nielsen,, Former Editor

D.R. Brillinger,, Former Editor

B.W. Silverman,, Former Editor

D.J. Trewin,, Former Editor

V.N. Nair,, Former Editor

W.F.M. de Vries,, Former Editor

E. Arjas., Former Editor

J. van Sinderen, Former Editor

In the last decade, calibration estimation has developed into an important field of research in survey sampling. Calibration is now an important methodological instrument in the production of statistics. Several national statistical agencies have developed software designed to compute calibrated weights based on auxiliary information available in population registers and other sources.

This paper reviews some recent progress and offers some new perspectives. Calibration estimation can be used to advantage in a range of different survey conditions. This paper examines several situations, including estimation for domains in one-phase sampling, estimation for two-phase sampling, and estimation for two-stage sampling with integrated weighting. Typical of those situations is complex auxiliary information, a term that we use for information made up of several components. An example occurs when a two-stage sample survey has information both for units and for clusters of units, or when estimation for domains relies on information from different parts of the population.

Complex auxiliary information opens up more than one way of computing the final calibrated weights to be used in estimation. They may be computed in a single step or in two or more successive steps. Depending on the approach, the resulting estimates do differ to some degree. All significant parts of the total information should be reflected in the final weights. The effectiveness of the complex information is mirrored by the variance of the resulting calibration estimator. Its exact variance is not presentable in simple form. Close approximation is possible via the corresponding linearized statistic. We define and use automated linearization as a shortcut in finding the linearized statistic. Its variance is easy to state, to interpret and to estimate. The variance components are expressed in terms of residuals, similar to those of standard regression theory. Visual inspection of the residuals reveals how the different components of the complex auxiliary information interact and work together toward reducing the variance.

After defining the concept of representativeness of a random sample, the author proposes a measure of how much the observed sample represents its parent distribution. This measure is called Representativeness Index. The same measure, seen as a function of a sample and of a distribution, will be called Representativeness Function. For a given sample it provides the value of the index for the different distributions under examination, and for a given distribution it provides a measure of the representativeness of its possible samples. Such Representativeness Function can be used in an inferential framework just as the likelihood function, since it gives to any distribution the ''experimental support'' provided by the observed sample. This measure is distribution-free and it is shown to be a transformation of the well-known Cramér-von Mises statistic. By using the properties of that statistic, criteria for providing set estimators and tests of hypotheses are introduced. The utilization of the representativeness function in many standard statistical problems is outlined through examples. The quality of the inferential decisions can be assessed with the usual techniques (MSE, power function, coverage probabilities). The most interesting examples turn out to be those of situations that are ''non-regular'', as for instance the estimation of parameters involved in the support of the parent distribution, or less explored (model choice).

Model selection criteria often arise by constructing unbiased or approximately unbiased estimators of measures known as expected overall discrepancies (Linhart & Zucchini, 1986, p. 19). Such measures quantify the disparity between the true model (i.e., the model which generated the observed data) and a fitted candidate model. For linear regression with normally distributed error terms, the "corrected" Akaike information criterion and the "modified" conceptual predictive statistic have been proposed as exactly unbiased estimators of their respective target discrepancies. We expand on previous work to additionally show that these criteria achieve minimum variance within the class of unbiased estimators.

Books on linear models and multivariate analysis generally include a chapter on matrix algebra, quite rightly so, as matrix results are used in the discussion of statistical methods in these areas. During recent years a number of papers have appeared where statistical results derived without the use of matrix theorems have been used to prove some matrix results which are used to generate other statistical results. This may have some pedagogical value. It is not, however, suggested that prior knowledge of matrix theory is not necessary for studying statistics. It is intended to show that a judicious use of statistical and matrix results might be of help in providing elegant proofs of problems both in statistics and matrix algebra and make the study of both the subjects somewhat interesting. Some basic notions of vector spaces and matrices are, however, necessary and these are outlined in the introduction to this paper.

A matrix trigonometry developed chiefly by this author during the past 40 years has interesting applications to certain situations in statistics. The key conceptual entity in this matrix trigonometry is the matrix (maximal) turning angle. Associated entities (originally so-named by this author) are the matrix antieigenvalues and corresponding antieigenvectors upon which the matrix obtains its critical turning angles. Because this trigonometry is the natural one for linear operators and matrices, it also is the natural one for matrix statistics.

Hyperparameter estimation in dynamic linear models leads to inference that is not available analytically. Recently, the most common approach is through MCMC approximations. A number of sampling schemes that have been proposed in the literature are compared. They basically differ in their blocking structure. In this paper, comparison between the most common schemes is performed in terms of different efficiency criteria, including efficiency ratio and processing time. A sample of time series was simulated to reflect different relevant features such as series length and system volatility.

The nonparametric graduation of mortality data aims to estimate death rates by carrying out a smoothing of the crude rates obtained directly from original data. The main difference with regard to parametric models is that the assumption of an age-dependent function is unnecessary, which is advantageous when the information behind the model is unknown, as one cause of error is often the choice of an inappropriate model. This paper reviews the various alternatives and presents their application to mortality data from the Valencia Region, Spain. The comparison leads us to the conclusion that the best model is a smoothing by means of Generalised Additive Models (GAM) with splines. The most interesting part of this paper is the development of a plan that can be applied to mortality data for a wide range of age groups in any geographical area, allowing the most appropriate table to be chosen for the data in hand.

The stochastic approach is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. Rather than just providing a single number for the rate of inflation, the stochastic approach provides the whole probability distribution of inflation. This paper reviews the key elements of the approach and then discusses its early history, including some previously overlooked links with Fisher's work contained in his book The Making of Index Numbers. We then consider some more recent developments, including Diewert's well-known critique of the stochastic approach, and provide responses to his criticisms. We also provide a review of Theil's work on the stochastic approach, and present and extend Diewert's work on this topic within the context of the Country Product Dummy method which measures price levels internationally. The paper also contains some recent material on the value of information from the perspective of the stochastic approach, as well as illustrative applications.

A new method for protecting microdata is introduced. This method, perturbation of unsafe combinations (Peruco), eliminates unsafe combinations in the records in which they occur, by replacing them with safe combinations that are also consistent with the other values in the remainder of the records. Consistency is relative to a set of micro-edits that is supposed to be given along with the microdata. A deterministic optimization model is discussed, as well as possible extensions.