Showing papers in "International Statistical Review in 1998"

Statistical Analysis of Product Warranty Data

Abstract: Summary Data bases regarding warranty claims for manufactured products record claims experience and information about concomitant factors. If constructed and maintained properly, warranty data bases may be used for a variety of purposes that include the prediction of future claims, the comparison of claims experience for different groups of products, the estimation of field reliability, and the identification of opportunities for quality and reliability improvement. This paper reviews some methods of analyzing warranty data and of addressing these objectives. Some extensions of previous work and suggestions for future development are included. Examples involving warranty claims for automobiles and refrigerators are considered.

Imputation: Methods, Simulation Experiments and Practical Examples

Abstract: Summary When conducting surveys, two kinds of nonresponse may cause incomplete data files: unit nonresponse (complete nonresponse) and item nonresponse (partial nonresponse). The selectivity of the unit nonresponse is often corrected for. Various imputation techniques can be used for the missing values because of item nonresponse. Several of these imputation techniques are discussed in this report. One is the hot deck imputation. This paper describes two simulation experiments of the hot deck method. In the first study, data are randomly generated, and various percentages of missing values are then non-randomly 'added' to the data. The hot deck method is used to reconstruct the data in this Monte Carlo experiment. The performance of the method is evaluated for the means, standard deviations, and correlation coefficients and compared with the available case method. In the second study, the quality of an imputation method is studied by running a simulation experiment. A selection of the data of the Dutch Housing Demand Survey is perturbed by leaving out specific values on a variable. Again hot deck imputations are used to reconstruct the data. The imputations are then compared with the true values. In both experiments the conclusion is that the hot deck method generally performs better than the available case method. This paper also deals with the questions which variables should be imputed and what the duration of the imputation process is. Finally the theory is illustrated by the imputation approaches of the Dutch Housing Demand Survey, the European Community Household Panel Survey (ECHP) and the new Dutch Structure of Earnings Survey (SES). These examples illustrate the levels of missing data that can be experienced in such surveys and the practical problems associated with choosing an appropriate imputation strategy for key items from each survey.

Random Sets: Models and Statistics

Abstract: Summary This paper surveys aspects of the theory of random closed sets, focussing on issues of practical and current interest. First, some historical remarks on this part of probability theory are made, where the important role of Georges Matheron is emphasized. Then, fundamental characteristics of the distribution of random closed sets are introduced. The very important Boolean model serves as an example for discussing mathematical and statistical problems. A number of further models is then considered, namely excursion sets of random fields, the system of edges of the Poisson Voronoi tessellation and various random systems of non-overlapping spheres. Finally, some ideas of particle statistics are presented, including some models of random compact sets.

Doing Least Squares: Perspectives from Gauss and Yule

Abstract: Summary Gauss introduced a procedure for calculating least squares estimates and their precisions. Yule introduced a new system of notation adapted to correlation analysis. This paper describes these formalisms and compares them with the matrix and vector space formalisms used in modern regression analysis.

Three Sides of Smoothing: Categorical Data Smoothing, Nonparametric Regression, and Density Estimation

Abstract: Summary The past forty years have seen a great deal of research into the construction and properties of nonparametric estimates of smooth functions. This research has focused primarily on two sides of the smoothing problem: nonparametric regression and density estimation. Theoretical results for these two situations are similar, and multivariate density estimation was an early justification for the Nadaraya-Watson kernel regression estimator. A third, less well-explored, strand of applications of smoothing is to the estimation of probabilities in categorical data. In this paper the position of categorical data smoothing as a bridge between nonparametric regression and density estimation is explored. Nonparametric regression provides a paradigm for the construction of effective categorical smoothing estimates, and use of an appropriate likelihood function yields cell probability estimates with many desirable properties. Such estimates can be used to construct regression estimates when one or more of the categorical variables are viewed as response variables. They also lead naturally to the construction of well-behaved density estimates using local or penalized likelihood estimation, which can then be used in a regression context. Several real data sets are used to illustrate these points. Resume Durant les quarantes derni1eres annees, I'estimation fonctionnelle nonparametrique a connuun developpement considerable ce travail presente, un bilan des recherches portant sur l'estimation des fonctions de densites et de regression. les regression. Les resultats theoriques associee ces deux problemes d'estimation sont tres similaires. De plus, l'estimateur de Nadaray-watson d'une fonction de regression trouve se racines dans I'estimation de densites multivariees. Un troisieme volet de I'estimation fonctionnelle, moins exploite, est celui de l'estimation par lissage de lois de probabilite de donnees categoriques. Ce travail explore le fait que ce type d'estimation constitue un pont entre I'estimation nonparametrique de densites et de estimateurs de lois de probabilites de donnees categoriques. Un choix adequat de la fonction de vraisemblance permet de construire des estimateurs possedant de nombreuses proprietes interessantes. les estimateurs ainsi obtenus peuvent âtre utilises en estimation de regression aussi bien dans le cas de variables reoibses categiruques ou dans le cas d'une estimation prealable de densites par le biais de la vraisemblance locale ou penalisee. les divers problemes abordes dans ce travauk sont illustres par l'entremise de plusieurs jeux de donneelles.

Bayesian Comparison of ARIMA and Stationary ARMA Models

Abstract: Summary Time series analysts have long been concerned with distinguishing stationary "generating processes" from processes for which differencing is required to induce stationarity. In practical applications, this issue is addressed almost invariably through formal hypothesis testing. In this paper, we explore some aspects of the Bayesian approach to the problem, leading to the calculation of posterior odds ratios. Interesting features arise in the simplest possible variant of the problem, where a choice has to be made between a random walk and a stationary first order autoregressive model. We discuss in detail the analysis of this case, and also indicate how our approach extends to the more general comparison of an ARIMA model with a stationary competitor.

On the Application of Conditional Independence to Ordinal Data

Abstract: Summary A special log linear parameterization is described for contingency tables which exploits prior knowledge that an ordinal scale of the variables is involved. It is helpful, in particular, in guiding the possible merging of adjacent levels of variables and may simplify interpretation if higher-order interactions are present. Several sets of data are discussed to illustrate the types of interpretation that can be achieved. The simple structure of the maximum likelihood estimates is derived by use of Lagrange multipliers. Resume On decrit une parametristaion adaptee particulierement aux des variables ordinales. En particulier celle-ci pemettra de guider l'operation commetn combiner les niveaux combiner les niveaux adjacents pour simplifier l'interpretation. une illustration des possibilites d'interpreinterpretation de la methode a plusiurs enseieurs ensembles de donnees est presentee. La methode de Largrange expose la structure des estimateurs de maximum vraisemblage.

Professional Development for Teachers of probability and Statistics: Into an Era of Technology

Abstract: Summary The focus of this paper is the professional development of teachers of probability and statistics at school level. Within a world where the statistics curriculum is changing at school level, the professional development needs of teachers of statistics are changing and the technology to meet these needs is changing as well. This paper reviews the work in the field, describes the development of a multimedia package for professional development of statistics teachers and looks to the future.

Combining Data from Surveys and Administrative Record Systems. The Norwegian Experience

Abstract: Summary At Statistics Norway administrative data have been extensively used in order to improve the quality of survey data. Various techniques have been used to reduce sampling variance and/or to reduce the effects of non-response. In the present article some of the most commonly used methods are being presented, and based on empirical rather than theoretical evaluations, we give our conclusions concerning their potentials and limitations. Resume Le Bureau Central de Statistique se sert abondamment d'informations administratives afin d'ameliorer la qualite de ses enquee. Diverses techniques ont ete utilisees pour les ecarts entre les echantillons et/ou reduire les effets de l'absence de resent article examine quelques-unes des methodes les plus couramment utilisees et, sur la base d'evaluations empiriques pluto que theoriques, liver nos conclusions sur les possibilite et les limites de ces methodes.

A Unified View of Signal Extraction, Benchmarking, Interpolation and Extrapolation of Time Series

Abstract: Les series chronologiques sont souvent soumises a des ajustements de nature statistique, requis pour en augmenter la precision, remplacer des valeurs manquantes et faciliter l'interpretation L'extraction de signal (e.g. lisssage), l'etalonnage, l'interpolation et l'extrapolation comptent parmis les ajustements les plus communs. Le present article presente un modele de regression dynamique et stochastique, a partir duquel la plupart de ces ajustements peuvent se faire; il prouve que l'estimateur par moindres carres generalises resultant est l'estimateur lineaire non-biaise de variance mimimum. L'article generalise aussi certaines methodes, afin de traiter les cas de signal mixte (avec composantes deterministe et stochastique) et d'erreurs autocorrelees et heteroschedastiques.

Estimation in Surveys Using Conditional Inclusion Probabilities: Simple Random Sampling

Abstract: Summary In survey sampling, auxiliary information on the population is often available. The aim of this paper is to develop a method which allows one to take into account such auxiliary information at the estimation stage by means of conditional bias adjustment. The basic idea is to attempt to construct a conditionally unbiased estimator. Four estimators that have a small conditional bias with respect to a statistic are proposed. It is shown that many of the estimators used in the literature in the case of simple random sampling can be obtained by using this estimation principle. The problem of simple random sampling with replacement, poststratification, and adjustment of a 2 x 2 dimensional contingency table to marginal totals are discussed in the conditional framework. Finally it is shown that the regression estimator can be viewed as an approximation of an application of the conditional principle. Resume Dans les enquetes par sondage, une information auxiliaire sur l'ensemble de la population est souvent disponible. Le but de cent aticle est de developper une methode qui permet de prendre en compte cette information auxiliaire a l'etape de l'estimation au moyen d'un ajustement du biais conditionnel. L'idee de base estde tenter de constuire un estimateur sans biaisconditionnel. Quatre estimateurs ayant un faible biais conditionnel sont proposes. On montre ensuite que beaucoup d'estimateus presentes dans la litterature dans le cas du plan simple sans remise peuvent etre obtenus en utilisant ce principe d'estimation. Les problemes du sondage aleatoire simple avec remise, de la poststratification, de l'ajustement d'un tableau de contigence de dimension 2 × 2 sont discutes dans le contexte de l'estimation conditionnelle. Finalement on montre que l'estimateur par la regression peut etre obtenu en cherchant une approximation de ce principe conditionnel.

The Measurement and Analysis of Poverty and Inequality: An Application to Spanish Conurbations

Abstract: Summary Poverty as a multidimensional phenomenon can be approached from different points of view. In this paper we study poverty in large towns in Spain taking into consideration three different definitions: a) relative monetary poverty, or scarcity of resources as compared with population averages, b) poverty measured through physical indicators, i.e. deprivation of certain goods, and c) subjective poverty. This last one appears'to be related to inequality, which-is also considered and analyzed. The source of statistical information used is the Spanish Household Budget Survey of 1990-91. Possibilities and drawbacks of this survey in the analysis of poverty and inequality are also reviewed. The French political scientist Alexis de Tocqueville (1835), while comparing poverty in several European countries hundred and fifty years ago, discovered what he considered a "very extraordinary and apparently inexplicable" fact: that countries appearing to be the most impoverished were those which in reality accounted for the fewest indigents, while in the richest countries, a considerable part of the population was obliged to rely on the gifts of others in order to live. The explanation that he gave to this apparent paradox was that the more developed a society is, the more involved the population becomes in industrial production. But employment in the industrial sector is usually precarious, and incomes generated by it are particularly sensitive to economic trends and fluctuations. Tocqueville's explanation probably accounts for the growing areas of poverty that tend to concen- trate in the large towns of industrialised countries. A diminishing workforce in industry, and a trend towards terciarization of employment are making social integration difficult for a considerable part of the population lacking the skills or ability to adapt to the rapidly changing demands of the labour market, thus generating a phenomenon known as "the new urban poverty". This is a research field of increasing interest. The detection of groups particularly prone to poverty, or poverty pockets, is an essential item of information for policy makers, as it allows them to decide which sectors of the population require particular assistance, and to evaluate afterwards the consequences of these decisions on individual welfare. Still, it is not an easy task. First because poverty in general is a difficult question both from the theoretical and the methodological point of view, as it usually includes not only physical deprivation but also the more subtle concept of social exclusion. And also because the statistical information available is not always appropriate to reflect

Reducing Costs of Censuses in Norway Through Use of Administrative Registers

Abstract: "For some years it has been the policy of Statistics Norway to collaborate with various governmental agencies in order to use administrative registers in statistics production. This policy has been supported politically, and a new Statistics Act has been useful in these efforts. The purpose of this paper is to present the strategy and methodology used to produce statistics in general, census statistics in particular, when based on a combined use of administrative registers and directly collected data. Experiences from Norwegian censuses since 1960 will be presented."

Studies on the Comparability of Consumer Price Indices

Abstract: Summary Comparability of statistical data between countries is a major objective for international statistical organisations such as EUROSTAT. The convergence criteria set down in the Maastricht Treaty explicitly require comparable consumer price indices in the European Union. We present an empirical analysis, largely based on simulations with Swedish and Finnish CPI data, of various potential sources of non-comparability, conceptual as well as technical ones. Resume La comparabilite des donnees statistiques, entre pays, est un objectif majeur des organismes statistques internationaux tels qu 'EUROSTAT. ainsi, les criteres de convergence pose par de masstricht exigent-ils des indices de prix a la consommation comparables dans l'union Europeenne. Nous presentons ici une analyse empirique, a partir de simulations sur les indices prix suedois et finlandais surtout, de diverses sources possibles de non-comparabilite, tant conceptuelle que technique.

Inferring Gene Ancestry: Estimating Gene Descent

Abstract: Summary Segregation indicators provide a fundamental description of the outcomes of Mendelian segregation This description facilitates algorithms for computation of probabilities of gene identity patterns among individuals in a specified genealogical structure Such gene identity patterns determine in turn the pattern of observable trait similarities among relatives Conversely, patterns of gene identity are the parameters of genealogical relationship that can be estimated from trait data on individuals Where data on large numbers of individuals or at large numbers of genetic loci are to be analyzed, Markov chain Monte Carlo realizations of underlying Mendelian segregation indicators can be used to provide Monte Carlo estimates of likelihoods for gene ancestry or of genetic model parameters Genealogical information in genetic data is bounded by the information in patterns of genomic identity by descent A different form of Monte Carlo likelihood can be used to assess this information Resume Les indicateurs de segregation nous fonurnissent une description fondamentale des resultats de la segregation mendelienne Cette description facilitte les algorithms pour le calcul des probabilites de structures d'identite des genes parmis les individus d'une structure gebealogique specifique Ces strucctures d'identite des genes determinent â leur tour les structures de similarite des traits obvservables parmis des gens de meme famille Inversement, les structures d'identite ds genes sont les parametres des relations genealogiques estimables a partir de donnes de traits d'individus Dans les cas oules donnes a analyser proviennent d'un grand nombre d'individus ou d'un grand nombre de loci genetiqus, des realiations Monte carlo de chaine de makov des indicateurs des indicateurs de segregation mendelienne sous-jacents peuvent etre utilises pour foumir ds estime Monte carlo de vraisemblance est limitee par l'information dans les satructures d'identite genomique origine une autre forme de vraisemblance Monte carlo peut etre utilisee pour evaluer cette information

Training Employees for African Statistical Offices

Abstract: Summary A review of the organizational set-up of a national statistical office, its staffing levels and subjects covered has been described. Two groups of employees of a statistical office are considered with respect to the teaching of statistics, namely those already in employment and those expected to be employed by a statistical office. The Statistical Training Programme for Africa (STPA), under which the present study was undertaken, improvement and strengthening of statistical training programmes for employees or expected employees of a statistical office, are described including selected aspects of the programme. Teaching programmes for those currently in employment with the objective of improving their work performance are also described. Achievements and problems of the programme are given. In conclusion a new framework for revitalisation of teaching of statistics in Africa in the 1990s is mentioned. Resume L'examen du cadre organisationnel d'un bureau national de la statistique, le nombre des personnels et les enseignements assures sont decrits. Deux groupes d'employes d'un bureau de la statistique ont ete consideres en ce qui concerne l'enseignement de la statistique. Ces employ'es comprennent ceux qui travaillent deja et ceux qui devraient etre recrutes par un bureau de la statistique. Le programme de formation en statistiques pour l'afrique (STPA), sous lequel ont ete entrepris l'amelioration et le renforcement des programmes de formation pour les employes d'un bureau de la statistique ou d ceux qui devraient etre recrutes par par un bureau de la statistaque, a ete decrit, y compris quelques aspects choisis du programe. les programmes d'ensignement qui visent l'amelioration de la perfommance ont ete indiques. En conclusion. un bibyveay cadre pour le renforcemnt de l'enseignemtn de la statistique en afrique en afrique au cours des 90 est proposeye.

I.J. Bienaymé [1796–1878]: Criticality, Inequality, and Internationalization*

Abstract: Summary Two striking contributions of Bienayme to mathematical statistics: (1) a completely correct statemet of the Criticality Theorem for simple branching processes in 1845; and (2) the derivation of the Bienayme-Chebyshev Inequality, are revisited on the 200th anniversary of his birth. We use writings and archival materials available since the note of Heyde & Seneta (1972) to present a fuller biographical picture. Bienayme's connections with Buniakovsky and Chebyshev are elucidated, and this role in furthering Chebyshev's international contacts outlined. A concluding section illuminates Bienayme's understanding of the linear regression of one random variable on another in an actuarial context of random shocks.

A Comment on The Creation of the Office for National Statistics by John Pullinger

Abstract: Summary This article establishes the availability of statistical information in Mexico. A good statistical information system is a necessary, not a sufficient condition for economic and social development. Resume Cet article etablie la disponibilite d'informations statistiques au Mexique. Une bonne information statistique est une condition necesaire mais non suffisante pour le developpement economique et social et pour eviter les crises financieres.