bluuebunny/crossref_metadata_2025 huggingface dataset:
Rules for building statistical models*
Authors: Hemelrijk J.
Published: April 2008

“Statistics uses the empirical hypothesis that apparatus (‘lotteries’) exist, admitting random choices of one among any given number of elements. Such apparatus do not exist in absolute perfection and their degree of perfection can only be defined after development of their theory. Their role is analogous to that of rigid bodies in euclidean geometry and of perfect clocks in dynamics. Empirical interpretation of probability statements is only possible with reference to such random apparatus or to natural phenomena empirically found to behave statistically sufficiently tike these”. D. van Dantzig [1]

Summary  One of the fundamental questions in statistical model building is when to use the same model for different situations or experiments. Axioms, however useful mathematically, say nothing about this. The author therefore proposes to introduce rules for the choice of a statistical model which have the character of instructions for use of the statistical toolkit. One of the basic rules proposed is the “principle of equivalence”. Two repeatable experiments are called statistically equivalent if they cannot be distinghuished from one another by means of sequences of outcomes of arbitrary length. This principle is elaborated and illustrated by means of an example. If experiments are (deemed to be) statistically equivalent the use of the same statistical model for all of them is justified. This principle is then used for the introduction of conditional probabilities and composite models, with symmetric probability spaces as models for randomizers as a startingpoint.
Analysis of three tests for one or two outliers
Authors: Hawkins Douglas M.
Published: April 2008

Summary  Three well‐known test statistics for the precense of two outliers are studied from the points of views of exact null distribution and power. In a sample case, it is shown that the Murphy two outlier statistic may suffer from masking. A recursive version of the Pearson‐Chandrasekar test is shown to perform well.
The proportional representation problem in the Second Chamber: an approach via minimal distances
Authors: Riele H. J. J. te
Published: April 2008

Abstract  The purpose of this paper is to discuss the proportional representation problem in the Second Chamber of Dutch Parliament. Firstly, the present procedure for solving this problem is described, together with a possible alternative procedure, recently proposed by F. J. Lisman. Next, the problem is formulated as that of minimizing some distance coefficient between the distribution of the votes of the electorate and that of the seats in the Second Chamber. For distances which satisfy a specific convexity condition a simple and straight forward algorithm is given for computing a distance minimizing seat distribution. The procedure of Lisman is shown to have three attractive properties by which it is distinguished from the other usual procedures for solving the proportional representation problem. Finally, the principle of the weighted vote is introduced as a means of breaking the deadlock which always comes into being, because of the inevitable discrepancy between the vote distribution and the actual seat distribution.
Indeterminacy problems and the interpretation of factor analysis results
Authors: Elffers Henk , Bethlehem Jelke , Gill Richard
Published: April 2008

Abstract  This paper reviews indeterminacy problems for the factor analysis model and their consequences for the interpretation of the results. Two types of indeterminacy are discerned: indeterminacy of the parameters in the model (the number of factors, the specific variances and the factorloadings) and the indeterminacy of the factors, given the parameters in the model. It is argued that parameter indeterminacy is partly to be overcome, provided that a strong underlying theory for the subject matter under research is present. Factor indeterminacy remains a major stumbling‐block for the interpretation of results. The Guttman criterion is advocated as a measure of factor indeterminacy.
A note on the extension of tables for the Friedman statistic
Authors: Sacks S. T. , Selvin S.
Published: April 2008

Abstract  The tables for the Friedman rank‐test arc extended using a sampling method. A table is given for the traditional significance levels .01, .025, .05 and .10 for number of blocks equal to 7 and 8 and for treatments of size 6 and 7. A brief discussion of available tables is also included along with an example of an application.
A Case Study of two Clustering Methods based on Maximum Likelihood
Authors: Ganesalingam S. , McLachlan G. J.
Published: April 2008

Abstract Two commonly used clustering methods based on maximum likelihood are considered in the context of the classification problem where observations of unknown origin belong to one of two possible populations. The basic assumptions and associated properties of the two methods are contrasted and illustrated by their application to some medical data. Also, the problem of updating an allocation procedure is considered.
The weighted empirical process of row independent random variables with arbitrary distribution functions
Authors: Shorack Galen R.
Published: April 2008

Abstract  The relative compactness and weak convergence of reduced empirical, quantile and weighted empirical processes are demonstrated under mild conditions. For example, the reduced empirical proces of arbitrary independent iv'S is always relatively compact in any ‖/q‖ metric with q square integrable; and weak convergence takes place if and only if the covariance function converges. Van Zuijlen's representation of the general empirical process is a fundamental tool. This paper both unifies and extends the previous treatment of these processes ‐ processes that have application to rank statistics and linear combinations of order statistics. Most proofs are contained in Section 3. A brief introduction to weak convergence is presented in the appendix for readers lacking this background. Applications are indicated in Section 4.
Maximum Likelihood Estimation of a Labour Demand System. An Application of a Model of Seemingly Unrelated Regression Equations with the Regression Errors Composed of Two Components
Authors: Verbon H. A. A.
Published: April 2008

Abstract  In this paper maximum likelihood estimation is applied to a system of labour demand equations. In view of the data used for estimation, the model of seemingly unrelated regression equations containing errors composed of two components which has been treated by Avery [1] is applied. Avery's results are presented and slightly generalized.
A large deviation result for the difference in sample medians
Authors: Rao P. V. , Wackerly D. D.
Published: April 2008

LetXmandYndenote the medians of independent samples from continuous populations Fand Grespectively. In Theorem 1 of this note, a large deviation result for the difference dmn= Xm‐ Ynis established under the assumption that Fand Garc symmetric about 0. The result is then used to define a sequential rule based on medians for selecting the best of Ksymmetric populations.
Thin layer chromatography, a case study
Authors: Akkerboom J.C. , Schepers P. , Werff J. v.d.
Published: April 2008

This paper gives an account of the collaboration between two mathematical statisticians and a toxicologist (the second author) interested in thin layer chromatography (TLC). A TLC “system” consists of a medium through which a solvent is transported. If a solution of some (toxic) sample is applied to the medium, then the components are carried forward by the solvent over different distances. Section 1 describes the concept of a data bank which provides standard values for the degrees of migration characteristic for each of mwell‐studied substances in each of nsystems. Sections 2–5 are mainly devoted to the construction of The “best design(s)”{j1*…jk*} of ksystems from the navailable ones. The attention is restricted to the situation that an unidentified sample exclusively contains one of the msubstances covered by the data bank and produces the scores xj…xjkin the systems j,…jkrespectively. Three different approaches to the identification problem were successively considered. Each approach leads to a class of procedures and their performances. The performance of the optimum procedure can be used to define the performance of any of the (nk) designs (j1…jk}. The latter performance is maximized in order to determine {j1*.,., jk*}. In practice usually data is obtained for mixtures instead of single. pure substances. Section 6 gives some tentative theory for the evaluation of such data.
On the Risk Performance of Bays Empirical Bayes Procedures for Classification Between N(‐1,l) and N(1,1)
Authors: Tsao How Jan
Published: April 2008

In empirical Bayes decision making, the Bayes empirical Bayes approach is diccussed by Gilliland and Boyer (1979). In the finite state component case, the Bayes empirical Bayes procedures are shown to have optimal properties in a fairly general setting and believed to have small sample advantage over the classical rules. The flexibility of making desirable adjustments for these decision procedures by choice of prior enables one to set a proper strategy when dealing with actual problems.

The applications of Bayes empirical Bayes procedures, however, create some interesting theoretical and computational problems as they are fairly complicated in structure. This paper gives a brief introduction into the Bayes empirical Bayes approach, and, to illustrate it, explicit results are given for testing H0: N(‐1,1) against H1: N(1,1).
Is recreation affecting the number of birds' nests? A case study
Authors: de Roos GerlofTh. , Schaafsma Willem
Published: April 2008

This paper presents some results arising out of the collaboration during 1974–1980 between an ornithologist (the first author) and a statistician. Attention is focussed on the question as to whether Tables 1 and 2 provide sufficient evidence for the existence of effects of recreation upon the numbers of oyster‐catcher nests and on the estimation of these effects by means of confidence intervals. The main tool is the standard theory for constructing conditional tests for multiparameter exponential families. The authors try to give a very careful description of the methodological aspects of their case. Many different probabilistic models can be proposed. Accordingly the statistical problems concerning tests and confidence intervals admit different mathematical formulations and (or) solutions.

It is now apparent that, during their collaboration, the authors did not always make the most appropriate choice of models and procedures. They went through several stages before arriving at the choices which are basic to the sections 2, …, 5. By outlining these stages in Section 6 and mentioning the methodological errors which were committed they hope that readers will beware of similar pitfalls.
Asymptotic optimality of all signed rank tests at infinity
Authors: Kremer Erhard
Published: April 2008

All signed rank tests are proved to have the same optimal BAHADUR efficiency, when the alternative tends to infinity. This result underlines the significance of the classical approach of comparing rank tests under local alternatives (comp. KREMER [7], [8]).
Canonical forms and tests of hypotheses: Part I: The general univariate mixed model
Authors: Roebruck P.
Published: April 2008

Abstract  A class of linear models is defined which contains many of the usual mixed and random models and allows the construction of tests for a wide class of hypotheses in a general manner. Characterizations are given for this class of models denoted as “regular linear models”. Problems of estimation are briefly touched and some aids to practical applications are given, followed by two examples.
Canonical forms and tests of hypotheses Part II: Multivariate mixed linear models
Authors: Roebruck P.
Published: April 2008

Abstract  In the literature on multivariate analysis of variance, exact test procedures are restricted to linear models with fixed effects only. In this paper tests are presented for multivarite linear hypotheses with respect to mixed models, which constitude a generalization of (univariate) regular models described by Roebruck (1982). Furthermore it is shown, that the matrices, which are used to compute the test statistics, can be derived from the univariate “sums of squares” in the same manner as in the case of fixed models. The applicability of this theory is demonstrated by two examples.
A uniform weak law of large numbers under π‐mixing with application to nonlinear least squares estimation
Authors: Bierens H. J.
Published: April 2008

Abstract  In Bierens (1981) we have derived a uniform weak law of large numbers for stochastically stable processes with respect to a finite‐dependent base. In this paper we show that this uniform weak law carries over to stochastically stable processes with respect to a, more general, φ‐mixing base. This generalization will be used for relaxing the conditions for weak consistency and asymptotic normality of nonlinear least squares estimators.
Modelling association football scores
Authors: Maher M. J.
Published: April 2008

Abstract  Previous authors have rejected the Poisson model for association football scores in favour of the Negative Binomial. This paper, however, investigates the Poisson model further. Parameters representing the teams' inherent attacking and defensive strengths are incorporated and the most appropriate model is found from a hierarchy of models. Observed and expected frequencies of scores are compared and goodness‐of‐fit tests show that although there are some small systematic differences, an independent Poisson model gives a reasonably accurate description of football scores. Improvements can be achieved by the use of a bivariate Poisson model with a correlation between scores of 0.2.
Minimax character of the two‐sample χ2‐test
Authors: Luschgy H.
Published: April 2008

Abstract  We consider the problem of testing equality of the mean vectors of two multivariate normal populations when covariates are present and the covariance matrix is known. As an application of the Hunt‐Stein theorem it is shown that the χ2‐‐test of level a maximizes, among all level a tests, the minimum power on each of the contours where the χ2‐‐test has constant power. A corollary is that the χ2‐‐test is most stringent level a.
Asymptotic normality in vacancies on a line
Authors: Runnenburg J. Th.
Published: April 2008

Abstract Covering a row of hooks by hats (one hat needs two adjacent hooks) by choosing for the next hat a pair of free hooks with equal probability from the free hooks, we encounterxn, the number of isolated hooks remaining uncovered. We prove thatxnis asymptotically normal.
An IPPS (inclusion probability proportional to size) sampling scheme
Authors: Deshpande M.N. , Prabhu‐Ajgaonkar S.G.
Published: April 2008

Abstract In this paper a sampling scheme for selecting a sample of size two is formulated where the inclusion probability of a population unit is proportional to its size.
On divergence and convergence of sums of nonnegative random variables
Authors: Smit J.C. , Vervaat W.
Published: April 2008

Abstract  If X1, X2,… are exponentially distributed random variables thenσ∞k= 1 Xk=∞ with probability 1 iff σ∞k= 1 EXk=∞. This result, which is basic for a criterion in the theory of Markov jump processes for ruling out explosions (infinitely many transitions within a finite time) is usually proved under the assumption of independence (see FREEDMAN (1971), p. 153–154 or BREI‐MAN (1968), p. 337–338), but is shown in this note to hold without any assumption on the joint distribution. More generally, it is investigated when sums of nonnegative random variables with given marginal distributions converge or diverge whatever are their joint distributions.
ALGORITHMIC METHODS FOR SINGLE SERVER SYSTEMS WITH REPEATED ATTEMPTS
Authors: de Kok A. G.
Published: April 2008

In many practical situations customers applying for service and finding the server busy will not join a queue, but make a new attempt to enter service after some time. In this paper we study single server systems with repeated attempts both for infinite‐source input and finite‐source input where the service times are general and the reattempt times are exponential. Numerically stable recursion schemes are derived by which the time‐average and customer‐average steady‐state probabilities can be effectively computed.
A SIMPLE TEST FOR UNIFORMITY
Authors: Dijkstra Jan B. , Rietjens Tjeu J. M. , Steutel Fred W.
Published: April 2008

Abstract A new and very simple test for uniformity is proposed. An exact formula for the distribution under H0 of the corresponding test statistic is derived. This formula is only suitable for computer‐oriented use. For other circumstances a table of critical values is given. The power of the test is compared with that of two well‐known alternatives: the χ2‐test and the Kolmogorov‐Smirnov test.
CONFIDENCE INTERVALS FOR TEST INFORMATION AND RELATIVE EFFICIENCY
Authors: Oosterloo Sebie
Published: April 2008

In latent theory the measurement properties of a mental test can be expressed in the test information function. The relative merits of two tests for the same latent trait can be described by the relative efficiency function, i.e. the ratio of the test information functions. It is argued that these functions have to be estimated if the values of the item difficulties are unknown. Using conditional maximum likelihood estimation as indicated by Andersen (1973), pointwise asymptotic distributions of the test information and relative efficiency function are derived for the case of dichotomously scored Rasch homogeneous items. Formulas for confidence intervals are derived from the asymptotic distributions. An application to a mathematics test is given and extensions to other latent trait models are discussed.
TRUE VERSUS MEASURED THEIL INEQUALITY
Authors: Odink J.G. , van Imhoff E.
Published: April 2008

This article deals with several problems that arise when the Theil coefficient of income inequality is computed in practice.

Aggregation of income data into brackets leads to an underestimation of the true Theil inequality, which is defined as the value of the coefficient as computed from individual income data. The assumption that the individual incomes are distributed according to a linear density function within the income brackets is suggested as a method to estimate this aggregation error. Calculations show that this method approximates the true aggregation error reasonably well.

Several methods are discussed concerning the treatment of negative incomes. In particular one can construct an income bracket that contains both negative and positive incomes and which in the summation formula is weighted with zero weight. Of all methods this procedure using the assumption of a linear density function within brackets, yields the highest value of the Theil coefficient and is thus preferred to the other alternatives.
ADAPTIVE ESTIMATION OF BINOMIAL PROBABILITIES UNDER MISCLASSIFICATION
Authors: Albers W. , Veldman H.J.
Published: April 2008

If misclassification occurs the standard binomial estimator is usually seriously biased. It is known that an improvement can be achieved by using more than one observer in classifying the sample elements. Here it will be investigated which number of observers is optimal given the total number of judgements that can be made. An adaptive estimator for the probability of interest is introduced which uses an estimator of this optimal number of observers, obtained without additional cost. Some simulation results are presented which suggest that the adaptive procedure performs quite well.
EMBEDDED MATRICES FOR FINITE MARKOV CHAINS
Authors: Overdijk D.A.
Published: April 2008

For an arbitrary subset A of the finite state space 5 of a Markov chain the so–called embedded matrix PA is introduced. By use of these matrices formulas expressing all kinds of probabilities can be written down almost automatically, and calculated very easily on a computer. Also derivations can be given very systematically.
THE CONSTRUCTION OF THE SIMPLE X2 AND NEYMAN SMOOTH GOODNESS OF FIT TESTS
Authors: Rayner J.C.W. , Best D.J. , Dodds K.G.
Published: April 2008

Suppose we wish to test whether data are consistent with a completely specified continuous distribution against a general alternative. Familiar omnibus tests are PEARSON'S X2 test and NEYMAN'S smooth test. Fundamental problems in the application of these tests are the construction and number of classes to use for X2, and the choice of the order of the NEYMAN smooth test. This paper examines these questions.
FORTY YEARS OF STATISTICS AND OPERATIONS RESEARCH IN THE NETHERLANDS
Authors: DOORNBOS R.
Published: April 2008

In 1985 we commemorate the fortieth anniversary of the V“VS, the Netherlands Society for Statistics and Operations Research. In this paper the contributions in our country during the post–war period to the theory of quantitative methods and to their applications are reviewed briefly.
VAN DE HULST ON ROBUST STATISTICS: A HISTORICAL NOTE
Authors: van Zwet W.R.
Published: April 2008

This paper provides a discussion of an unpublished set of notes written in 1942 by the Dutch astronomer H.C. VAN DE HULST. In these notes VAN DE HULST derives the asymptotic variances of M–estimators as well as trimmed means and concludes that the asymptotic variance of what is now called HUBER'S estimator is the same as that of a trimmed mean. This conclusion is usually ascribed to BICKEL (1965). A letter written by D. VAN DANTZIG in 1943 providing a critical evaluation of. VAN DE HULST'S results, adds interest to this suprisingly early contribution to the theory of robust statistics.
ERRORS IN VARIABLES IN ECONOMETRICS: NEW DEVELOPMENTS AND RECURRENT THEMES*
Authors: BEKKER P.A. , WANSBEEK T.J , KAPTEYN A.
Published: April 2008

The paper reviews some old and new approaches to the analysis of linear models with errors in variables. The emphasis is on the identification problems that usually arise in errors–in–variables models and on the various types of additional information that econometricians have invoked to be able to estimate parameters consistently. The approaches discussed include instrumental variables, grouping, simultaneous equations, multiple equations and bounds on measurement error variances.
A SURVEY OF THE EVOLUTION OF QUEUEING THEORY
Authors: Cohen J.W. , Boxma O.J.
Published: April 2008

The evolution of queueing theory is sketched from its origin in Teletraffic, via its growth to maturity as a mathematical discipline in Operations Research, to its present position as an indispensable tool in the performance analysis of complex computer—and communication networks. The Dutch postwar contributions to this evolution receive some special attention, on the occasion of the celebration of the Dutch Society for Statistics and ‘Operations Research’ fourth decennium.
BIOSTATISTICS IN MEDICINE
Authors: van Strik R. , van Stnk R. , Bezemer P.D.
Published: April 2008

This paper surveys the field of biostatistics in medicine as it has developed in the Netherlands. We look into the recent past and the present, and try to foresee future developments.
DESIGNING EXPERIMENTS TO FIT AND VALIDATE REGRESSION MODELS
Authors: Hoekstra J.A.
Published: April 2008

A graphical procedure is proposed for selecting designs suitable for estimation and validation of linear regression models. The procedure is exemplified with polynomial regression involving one and two explanatory variables.
A POISSON PROCESS APPROXIMATION FOR GENERALIZED K–S CONFIDENCE REG
Authors: Arsham H. , Miller D.R.
Published: April 2008

One–sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov–Smimov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This approximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modelling, and analysis of fault–tolerant systems.
EXTERNAL PIVOTING IN THE SIMPLEX ALGORITHM*
Authors: Eiselt H.A. , Sandblom C.‐L.
Published: April 2008

In this paper we describe the principle of external pivoting, a variant of the primal simplex algorithm. Its validity is proved in general and various strategies are designed which are based on this principle. The average convergence behavior for these strategies is then tested in a series of randomly generated problems. It is found that at least one of the strategies compares favorably with the regular simplex method.
A DISPLACED POISSON PROCESS APPLIED TO SCREENING FOR BREAST CANCER EN STRATIFIED SAMPLES WITH FALSE NEGATIVES*
Authors: Clarkson D.B. , Wolfson D.B.
Published: April 2008

A displaced Poisson process model allowing for stratified populations and “false negatives” is presented for describing the progress of certain chronic diseases. This model, which builds on earlier work by the authors, allows for the simple estimation of various parameters and distributions of interest in screening. A Monte Carlo simulation study illustrating and partially verifying the model predictions is given.
SPLIT–PLOT DESIGN: MODEL AND ANALYSIS FOR COUNT DATA
Authors: Engel J.
Published: April 2008

The analysis of count response data from designed experiments is well–known for independent response variables having the Poisson distribution. For experimental designs where responses are dependent, no general results seem to be available. An example of this type of design is the split–plot design, where sub–plot responses are essentially dependent within whole plots.

In this paper, a model will be proposed for split–plot count data and a separate analysis for whole plot and sub–plot data will be presented. It is interesting to note, that the same model is used in the quite different context of consumer buying behaviour. It is derived by Goodhardt, Ehrenberg and Chatfield and it was called the ‘Dirichlet model’, as the Dirichlet multinomial distribution, together with the negative binomial distribution, build up the model.
A STOCHASTIC PROCESS THAT IS AUTOREGRESSIVE IN TWO DIRECTIONS OF TIME.
Authors: de Haan L.
Published: April 2008

A continuous time stationary process is discussed that is maxautoregressive in one direction of time and sum–autoregressive in the other direction. A discrete time version of the process was discussed in Chemick (1981). A related continuous time process is discussed in Weiss (1980).
RECENT PH.D THESIS IN THE NETHERLANDS
Authors: SCHRIEVER B.F. , de JONG P.M.
Published: April 2008

Order dependence On June 21, 1985, B.F. Schriever received the doctors degree in the mathematical and physical science from the Vrije Universiteit at Amsterdam. Promotor and copromotor were Prof. Dr. J. Oosterhoff and dr. R.D. Gill and referent was Prof. Dr. J. de Leeuw. His thesis was prepared at the Mathematisch Centrum and at the Vrije Universiteit, both at Amsterdam.
A DISTRIBUTION–FREE CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN QUANTILES WITH CENSORED DATA
Authors: Chakraborti S. , Desu M. M.
Published: April 2008

Abstract. In the context of a two–sample problem, a confidence interval for the difference of appropriate quantiles of the two survival distributions is described. This method is especially useful when the data include some right–censored observations. A relevant mathematical result is proved.
PERFORMANCE OF MURPHY'S TEST FOR TWO OUTLIERS IN A LINEAR MODEL
Authors: Lalitha S. , Joshi P.C.
Published: April 2008

Abstract. In JOSHI and LALITHA (1986) a test for two outliers in the same direction in a linear model is discussed. Here the performance of this statistic is studied. For this, the exact non–null density function of the random variables involved in defining the statistic is obtained. Then a measure of performance is defined and it is applied to the case of a random sample from a normal distribution, as in this case the above said statistic reduces to the well known Murphy's test statistic. These values are then compared with the power values obtained by HAWKINS (1978).
ON THE UNIMODALITY OF GENERALIZED POISSON DISTRIBUTION
Authors: Consul P.C. , Famoye F.
Published: April 2008

Abstract. The unimodality property is very important in many statistical problems. In this paper, it is shown that the generalized Poisson distribution is unimodal. Upper and lower bounds to the mode are given.
THE APPROPRIATE REDUCTION OF THE WEIGHTED EMPIRICAL PROCESS
Authors: Shorack G.R. , Beirlant J.
Published: April 2008

Abstract. Using a new transformation (note (8)) to reduce down to [0,1], it is shown that the weighted empirical processes on [0,1] are always tight. This is shown to arise naturally through a discussion of a new inequality of MARCUS and ZINN (1984).
SUCCESSIVE MEASUREMENT EXPERIMENTS
Authors: Keen A. , Thissen J.T.N.M. , Hoekstra J.A. , Jansen J.
Published: April 2008

Abstract. We consider methods for the analysis of successive measurements, with emphasis on practical usefulness. It is described how the methods can be applied by using common techniques like regression analysis and analysis of variance.
RECURSIVE AND RELATED RESIDUALS
Authors: Loynes R.M.
Published: April 2008

Abstract.Recursive residuals are extended to the case that observations may occur in groups, which are ordered in time, but within which there is no time ordering. Analogous quantities are considered for two–dimensional ‘time’, for the balanced two–way table. Examples of their use are given.
ORDERING OF RISKS AND WEIGHTED COMPOUND DISTRIBUTIONS
Authors: Goovaerts M. J. , Vandebroeck M. , Kaas R.
Published: April 2008

Abstract. Some invariance properties of net stop loss ordering of risks are examined and proved in the framework of weighted compound distributions.
Polyhedral Combinatorics in Combinatorial Optimization
Authors: Gerards A.M.H. , Kolen A.W.J.
Published: April 2008

Polyhedral combinatorics is a subarea of combinatorial optimization of increasing practical importance. It deals with the application of the theory of linear systems and linear algebra to combinatorial problems. The paper is not intended as a survey on polyhedral combinatorics but it reviews some of the main concepts and proof techniques.
Randomized Response Techniques: A Review
Authors: Chaudhuri A. , Mukherjee R.
Published: April 2008

Randomized response techniques (RRT) are well–known as tools to procure trustworthy survey data on confidential issues. A review is attempted here of mostly published accounts on RRT covering qualitative and quantitative characters. Conflicting criteria of efficient estimation and protection of privacy are discussed. Infinite hypothetical and concrete finite population set–ups are treated separately.
Log–Linear Mixed Models for Categorical Data
Authors: Fidler V.
Published: April 2008

A method for construction of mixed models for categorical responses is described and its use is exemplified for three experimental designs: the repeated–measurements design, the change–over design and a design used for measurement of inter–observer agreement. The method may be viewed as an extension of the standard log–linear model methodology.
Nonparametric estimation of variance, skewness and kurtosis of the distribution of a statistic by jackknife and bootstrap techniques
Authors: Schemper M.
Published: April 2008

While jackknife and bootstrap estimates of the variance of a statistic are well–known, the author extends these nonparametric maximum likelihood techniques to the estimation of skewness and kurtosis. In addition to the usual negative jackknife also a positive jackknife as proposed by BERAN (1984) receives interest in this work. The performance of the methods is investigated by a Monte Carlo study for Kendall's tau in various situations likely to occur in practice. Possible applications of these developments are discussed.
Economic Process Control
Authors: Arnold B.F. , Iani E. von Col
Published: April 2008

A simple method is developed how to determine a nearly optimal economic sampling design tor current process control. A comparison between Shewhart and non Shewhart techniques reveals that under the assumptions of a normally distributed quality characteristic and an exponentially distributed time of production in the state of control the superiority of non Shewhart techniques is in general of no importance.
Statistical Problems in Ancient Numismatics
Authors: Stam A.J.
Published: April 2008

In antiquity coins were struck by placing a heated coin blank between two dies and hitting the upper die with a heavy blow of a hammer. When a die wore off, a new one was engraved. So dies intended to be the same show small differences that may be observed on extant coins as “the varieties”. Numismatists collect statistics of die varieties in as large a sample as possible of extant coins of a single issue they can find to study. From these statistics they want to estimate the number of dies used in producing the coin issue. To do this they need a parametric stochastic model describing how coins survive and become part of the sample. Several models are tried and tested against the data of two large samples, one of them new. (Few large samples exist). Estimators are reviewed and some related statistical problems studied.
A Path Construction for the Virtual Waiting Time of an M/G/1 Queue
Authors: Hooghiemstra G.
Published: April 2008

Consider the M/G/1 queue, the finite dam M/G/1 with capacity T, and the impatient customer M/G/1 model, where customers become lost customers if their waiting time exceeds τ. In this note we prove that for all three models and each xe(0, r) the distribution of the number of downcrossings of the virtual waiting time process with level x during a busy cycle is identical. This implies the weaker statement that on [0, T) the distribution functions of the steady state distributions of the amount of unprocessed work (virtual waiting time) are proportional. A number of applications is given.
On the relative precision of several allocations in stratified sampling
Authors: Moors J.J.A.
Published: April 2008

MOORS (1973) gave lower bounds for the relative precision of different allocations compared to Neyman allocation in stratified sampling. These results are extended here to the relative precision with respect to optimal allocation. A result of COCHRAN (1977) is generalized.
Exceptional Convergence of the Sample Variance
Authors: Moothathu T.S.K.
Published: April 2008

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S2 is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S2 is shown to converge in distribution to (1 –V)√2, where V has chi–square distribution with one degree of freedom.
Formal statistics and informal data analysis, or why laziness should be discouraged
Authors: Molenaar I.W.
Published: April 2008

The paper gives a personal view on how empirical research and subsequent data analysis and reporting should ideally proceed. Although the introduction concedes that practical limitations and imperfect knowledge usually impose restrictions on our possibilities to approximate this ideal situation, it is argued that investigators and statistical consultants should make a strong effort to come close to it. At the stages of design, analysis, and reporting, this requires careful consideration of the selection of the units of analysis, the choice of variables to be included, their measurement process, and the extent to which relevant assumptions are fulfilled. In so far as exploratory data analysis techniques offer the suggestion that they can produce results without such careful consideration, their use should be discouraged unless they are followed by a confirmatory analysis in which the claims of generalizability are better substantiated. Some protest is raised against the idea that the data themselves have a clear structure lying ready to be unveiled by the investigator by means of some numerical or spatial representation, which would permit to draw general conclusions.
Models and techniques
Authors: de Leeuw J.
Published: April 2008

In the situations typically encountered in the social sciences the methodology of traditional statistics is neither a good description of data analysis practice nor a good prescription to arrive at satisfactory summaries of the data. On the other hand the traditional statistical techniques are excellent data analysis tools, and statistical models are useful devices that can be used to develop and evaluate data analysis techniques. These general considerations are applied in this paper to evaluate the usefulness of techniques such as multidimensional scaling and correspondence analysis.
A robust scale estimator based on the shortest half
Authors: Rousseeuw P.J. , Leroy A.M.
Published: April 2008

A new robust estimator of scale is considered, which is proportional to the length of the shortest half of the sample. The estimator is compared to the interquartile range and the median absolute deviation, that are also based on order statistics. All three estimators have the same influence function, but their breakdown points differ. It also turns out that one needs a finite‐sample correction factor which depends on mod(sample size, 4) to achieve approximate unbiasedness at normal distributions.
Characteristic properties of order statistics based on random sample size from an exponential distribution
Authors: Ahsanullah M.
Published: April 2008

Suppose X1, X2, Xm is a random sample of size m from a population with probability density function f(x), x > 0), and let X1, m< × 2, m <… < Xm, m be the corresponding order statistics.

We assume m is an integer‐valued random variable with P(m=k) =p (1‐p)k‐1, k= 1,2,… and 0 < p < 1. Two characterizations of the exponential distribution are given based on the distributional properties of Xl, m.
Interpolation and optimal linear prediction
Authors: Corsten L.C.A.
Published: April 2008

This paper is concerned with the interpolation of spatially distributed observations of a quantitative phenomenon, sometimes referred to as kriging. This activity can be understood as a prediction procedure for values of random functions under stationarity assumptions in a polynomial linear regression context. After a heuristic and an exact derivation of the best linear unbiased prediction procedure (and the variance of prediction error) if the covariance function relating covariance between two possible observations to their mutual distance is known, follows the introduction of weaker assumptions admitting the definition of the variance only for increments of a certain order by a pseudoco–variance function. A particular related case is the so–called semivariogram for increments of order one. The prediction procedure turns out to be similar to that in the previous situation. The weaker assumptions allow an unbiased estimation of the unknown pseudocovahance function of polynomial form under restrictions imposed by Fourier transformation. Extension from point–wise observations or predictions to area or volume averages is touched upon.
Some results on discrete a–monotonicity
Authors: Alzaid A.A. , Al–Osh D.A.
Published: April 2008

Some characterizations and preservation properties of a–monotonicity are investigated. In particular it is shown that a mixture of binomial or Poisson distributions preserves the a–monotonicity of the mixing distribution. Also, a characterization of a class of infinitely divisible distributions, within the discrete α–unimodal class, is given. This characterization is the discrete version of that of ALAMATSAZ (1985) and KOTZ and STEUTEL (1988) in the continuous case.
A parallel insertion heuristic for vehicle routing with side constraints
Authors: Savelsbergh M.W.P.
Published: April 2008

In the early eighties, Fisher and Jaikumar developed a generalized assignment heuristic for vehicle routing problems. In this paper, we discuss some of the strong and weak points of this heuristic, and take its basic ideas to develop a new parallel insertion heuristic for the vehicle routing and scheduling problem that is better able to handle various side constraints.
Quasi‐likelihood inference in a generalized linear mixed model for balanced data
Authors: Engel J.
Published: April 2008

For modelling the effect of crossed, fixed factors on the response variable in balanced designs with nested stratifications, a generalized linear mixed model is proposed. This model is based on a set of quasi‐likelihood assumptions which imply quadratic variance functions. From these variance functions, deviances are obtained to quantify the variation per stratification. The effects of the fixed factors will be tested, an dispersion components will be estimated. The practical use of the model is illustrated by reanalysing a soldering failures problem.
Latent variables in econometrics
Authors: Kmenta J.
Published: April 2008

Unobservable variables in econometrics are represented in one of three ways: by variables contaminated by measurement errors, by proxy variables, or by various manifest indicators and/or causes. This paper contains a discussion of models involving each of these representations, and highlights certain interesting implications that have been insufficiently emphasized or completely unrecognized in the literature.
Nonparametric density estimation with grouped observations
Authors: Eilers P. H.C.
Published: April 2008

A smooth and detailed distribution is fitted to coarsely grouped frequency data by a nonparametric approach, based on penalized maximum likelihood. The estimated distribution conserves mean and variance of the data. The numerical solution is described and a compact and simplified algorithm is given. The procedure is applied to two empirical datasets.
Significance levels of linear rank tests using Edgeworth expansions
Authors: Christmann A. , Gather U.
Published: April 2008

We study one aspect of applying Edgeworth expansions to linear rank statistics. Since the use of such expansions is often recommended already for moderate sample sizes we investigate for this case the gain of accuracy for the level of significance of some linear rank tests when their critical values are derived from an Edgeworth expansion instead of from a normal approximation. We verify Does' conditions (1983) for the validity of the expansions for four rank statistics of general interest and show by a numerical study that an Edge‐worth expansion does not outperform the normal approximation in all situations. A considerable improvement shows up however for the Klotz test at the 5% level.
Disclosure risk for microdata stemming from official statistics
Authors: Blien U. , Wirth H. , Muller M.
Published: April 2008

In the research project on data anonymity, the possibilities and difficulties of restoring the identity of respondents, whose data have been anonymized, were tested in realistic simulations. In this paper the results of an application of a) a matching procedure and of b) a method based on discriminate analysis are reported. In the experiments carried out, empirical data of a handbook about German scientists and scholars and the German microcensus were used. A check of the results by an independent data‐trustee demonstrated that a real intruder has more difficulties achieving an identification than is frequently assumed.
On subset selection from logistic populations
Authors: van der Laan P.
Published: April 2008

Some distributional results are derived for subset selection from logistic populations, differing only in their location parameter. The probability of correct selection is given. Exact and numerical results concerning the expected subset size are presented.
A Central Limit Theorem for M‐estimators by the von Mises Method
Authors: Heesterman C.C. , Gill R.D.
Published: April 2008

Asymptotic normality of M‐ or maximum likelihood type estimators was established in a classic paper by Huber (1967). Reeds (1976) argued that this could have been obtained simply as an application of the delta‐method, using the tool of compactly differentiating von Mises functionals with respect to the empirical distribution function Fn. His proof however contains some errors and has been largely ignored. A corrected version of the proof is given.
Asymptotic linearity of minimax estimators
Authors: van der Vaart A.W.
Published: April 2008

The celebrated local asymptotic minimax (LAM) theorem due to HÁjek (1972) also includes the statement that a LAM estimator Is necessarily asymptotically linear. A similar result. is true for semi‐parametric models, but Hájek's result doesn't apply to this case as the efficient influence function is often not contained in the (proper) tangent space. This note gives a simple, elementary proof of both the LAM theorem and the necessity of asymptotic linearity of a LAM estimator sequence.
Aspects of statistical computing, past, present and future
Authors: Nelder J. A.
Published: April 2008

The various stages in the history of statistical computing are illustrated by personal experiences. The stages include batch processing, interactive working, and the consultative mode. Statistical aspects associated with one or more of these stages include the development of general algorithms, procedures for model checking, and data‐driven non‐parametric modelling.
Computer algebra in probability and statistics
Authors: Kendall W. S.
Published: April 2008

This paper discusses the uses of computer algebra within statistics and probability. A distinction is drawn between the use of computer algebra packages tosupportinvestigations, by performing calculations, ankl their use toimplement structure;to build in elements of a theory (such as stochastic calculus or the Taylor string theory of Barndorff Nielsen and others) as a preliminary to research investigations. Brief surveys are given of instances in the literature of use of computer algebra in probability and statistics. Two examples of implementations of structure are discussed, both drawn from the author's own work with the computer algebra package REDUCE. One is a simple demonstration using moments of the Poisson distribution. The other isitovsn3, an implementation of the semimartingale stochastic calculus. It is described howitovsn3may be used to derive the characteristic function of the Lévy stochastic area, following a proof due to S. Janson. Prospects for future work and for work in progress are discussed.
Some applications of the fast Fourier transform algorithm in insurance mathematics This paper is dedicated to Professor W. S. Jewell on the occasion of his 60th birthday
Authors: Embrechts P. , Grübel R. , Pitts S. M.
Published: April 2008

Transform methods, together with the fast Fourier transform algorithm, can be used to compute various quantities of interest in risk theory and insurance mathematics. These include the total claim size distribution at a fixed time, the mean and variance of the claim size process as a function of time in the Sparre‐Andersen model, and the probability of ruin. The associated discretization error can be reduced by applying Richardson's deferred approach to the limit. A theorem is given that puts the use of this technique on a mathematical basis in the context of compound distributions.
Recent Ph.D. Theses in the Netherlands
Authors: Dol Wietse
Published: April 2008

Statistica Neerlandica has decided to encourage the reporting on theses in probability, statistics, biometrics, econometrics, and operations research, submitted to Dutch universities. The main purpose of this section is to inform the reader briefly of the nature, the practical and theoretical importance, the methods used, and the results presented in recent theses. It is understood that contributions to this section meet with the approval of the supervisor(s) of the thesis.

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