bluuebunny/crossref_metadata_2025 huggingface dataset:
The rate of convergence in distribution of the maxima
Authors: Davis Richard A.
Published: April 2008

Abstract  Assume the normalized maxima, from an independent and identically distributed sequence of random variables, converge in distribution to a non‐degenerate random variable with extreme value distribution G(x). We derive a pointwise rate for this convergence which holds for all n and x with G(x) > 0. A closer examination of this result suggests how a uniform rate can be obtained.
Asymptotic confidence intervals for the effect of closing an area upon the number of birds' nests
Authors: Jong Paul M. de
Published: April 2008

Abstract  The methodological discussion in De Roos‐Schaafsma (1981) Section 6 is continued by proposing asymptotic methods as a substitute for laborious confidence interval computations.
The life‐length of banknotes*
Authors: Koeze P.
Published: April 2008

Abstract  With the aid of the Bank's banknote sorting system the issue and subsequent withdrawal of f 25–banknotes on three varieties of paper have been recorded for two‐and‐a‐half years. The aim was to measure the durability of the three paper varieties in circulation. The results of this second trial with f 25–banknotes confirm the statistical model developed previously for the first trial with f 100–banknotes. GRESHAM's Law is equally not applicable, neither to f 25–banknotes nor to f 100–banknotes. A two‐parameter gamma distribution fits the cumulative fraction of banknotes withdrawn reasonably well.
A Review of Simultaneous Painvise Multiple Comparisons
Authors: Games P. A. , Keselman H. J. , Rogan J. C.
Published: April 2008

Abstract  A Review of Simultaneous Pairwise Multiple Comparisons. Simultaneous pairwise comparisons can be accomplished with numerous multiple comparison procedures. The methods differ in two essential ways: the choice of critical value and the specification of the estimated standard error of the mean difference. Those methods that assume homogeneous variances are not robust to violations of this assumption. The methods are contrasted via a numerical example. Results of recent Monte Carlo work are described. A choice between the Games‐Howell, Dunnett, and Cochran procedures is recommended.
A nonparametric k‐sample test for data defined by intervals
Authors: Schemper M.
Published: April 2008

Abstract  If observations are restricted in such a way that only intervals covering the true but hidden values are known and k‐samples are to be compared by location, the use of a generalized Kruskal‐Wallis test is suggested.
Random number generators for a pocket calculator*
Authors: Es A.J. Van , Gill R.D. , Putten C. Van
Published: April 2008

Abstract  Some theory of linear congruential pseudo random number generators xn+1= (axn+c) mod m is summarized for the case in which the modulus m is a power of 10. These generators are especially suitable for implementation on both programmable and non‐programmable pocket calculators. Results are presented of extensive statistical testing of two specific generators.
The asymptotic behaviour of the estimated generalized least squares method in the linear regression model
Authors: Genugten B.B. Van Der
Published: April 2008

Abstract  In the linear regression model the generalized least squares (GLS) method is only applicable if the covariance matrix of the errors is known but for a scalar factor. Otherwise an estimator for this matrix has to be used. Then we speak of the estimated generalized least squares (EGLS) method. In this paper the asymptotic behaviour of both methods is compared. Results are applied to some standard models commonly used in econometrics
On the prehistory of Correspondence Analysis
Authors: Leeuw J. de
Published: April 2008

Abstract  The early history of correspondence analysis is reviewed. It is shown that K. Pearson came very close to discovering correspondence analysis in 1906. That he did not actually discover it may be because he was not familiar with the singular value decomposition, which is the basic existence result in correspondence analysis.
Mean, Median, Mode III*
Authors: Dharmadhikari S. W. , Joag‐dev K.
Published: April 2008

Abstract  Recently, Van Zwet (1979) has discussed several conditions under which the celebrated mean‐median‐mode inequality holds. This note points out that Van Zwet's basic condition and its variants have a simple interpretation in terms of a well‐known stochastic ordering. The results are slightly more general than Van Zwet's because the definition of unimodality used here (due to Khintchine) requires neither the existence of a density nor the uniqueness of the mode.
On iterative procedures of asymptotic inference
Authors: Dzhaparidze K. O.
Published: April 2008

Abstract  An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then for asymptotically efficient inference finitely many iterations are needed.
ON THE DISTRIBUTION OF ORDER STATISTICS FOR A RANDOM SAMPLE SIZE
Authors: Gupta D. , Gupta R. C.
Published: April 2008

The distributions of the life lengths of a parallel and of a series system with a random number of components have been studied in reliability theory. In this paper we obtain the distributions of the i'th order statistics and the range, assuming the sample size to be random, with a generalized negative binomial, a generalized Poisson and a generalized logarithmic series distribution. The results of Raghunandanan and Patil (1972) follow immediately from our results.
THE ASYMPTOTIC BEHAVIOR OF SIMPLE LINEAR RANK STATISTICS
Authors: Does Ronald J. M. M.
Published: April 2008

The concept of a simple linear rank statistic is essential in nonparametric theory. These statistics may be used for testing the null‐hypothesis that all observations are independent and identically distributed against classes of alternatives indicated by the choice of regression constants and scores. Special cases are the two‐sample Linear rank statistics and Spearman's rank correlation coefficient rho under the null‐hypothesis of independence.

In this paper we shall give a survey of the asympotic distribution theory of simple linear rank statistics.
MODELS FOR RESPONSE DATA SHOWING EXTRA‐POISSON VARIATION
Authors: Engel Jan
Published: April 2008

When count data show extra‐Poisson variation, standard log‐linear techniques to analyse the data may fail. In ihis paper a generalization of the log‐linear modelling technique is proposed for the negative binomial model, as an extension of the Poisson model. An illustration is given by the analysis of a twoway classification of soldering failure data; extensions to more general classifications are possible.
ASYMPTOTIC ABSOLUTE EFFICIENCY OF PROJECTION TESTS WITH AN APPLICATION TO N‐RANKING TESTS
Authors: Rothe Günter
Published: April 2008

A class of χ2‐type goodness‐of‐fit tests for the hypotheses of equal cell probabilities is introduced and the quality of the tests under arbitrary model restrictions is compared, where a suitable efficiency concept is used. As a special case, several nonparametric tests on treatment effects in the randomized block design can be considered. Some well known cases, such as the Anderson‐, Friedman‐ and the Page‐test, turn out to possess a certain minimax efficiency property under reasonable model assumptions. Finally a direct comparison between the Anderson‐ and Friedman‐tests is given.
THE JOINT ARRIVAL AND DEPARTURE PROCESS FOR THE M/M/l QUEUE
Authors: Boxma O. J.
Published: April 2008

We consider the M/M/1‐queue and derive an explicit expression for the joint distribution of the number of arrivals and the number of departures in [0, t), given the number of customers initially present. The derivation is almost purely combinatorial, it avoids the use of generating functions, and immediately yields a simple probabilistic interpretation of the result.
ON THE DISTRIBUTIONS OF ORDER STATISTICS FOR A RANDOM SAMPLE SIZE*
Authors: Consul P.C.
Published: April 2008

The probability distribution of the i –th and j–th order statistics and of the range R of a sample of size n, taken from a population with probability density function f (x) have been obtained when the sample size n is a random variable N and has: (i) a generalized Poisson distribution; and (ii) a generalized negative bonimial distribution. Specific results are then obtained; (a) when f (x) is uniform over (0,1); and (b) when f(x) is exponential. All the results for N, being a Poisson, binomial and negative binomial rv follow as special cases.
THE DISTRIBUTION OF GENERAL QUADRATIC FORMS IN NORMA
Authors: Dik J.J. , de Gunst M.C.M.
Published: April 2008

For a general quadratic form in normal variables a representation in terms of independently distributed standard normal variables is derived. The necessary and sufficient conditions for such a quadratic form to have a non–central chi–squared distribution can be found easily using this representation.
THE INDICATOR FUNCTION: A USEFUL DEVICE FOR DETERMINING CERTAIN MINIMAL SUFFICIENT STATISTICS
Authors: Laubscher N.F.
Published: April 2008

An elegant technique for obtaining minimal sufficient statistics in the case of families of distributions with support depending on the paramaters, is exposed.
THE BIVARIATE EXPONENTIAL DISTRIBUTION; A REVIEW AND SOME NEW RESULTS
Authors: Barnett V.
Published: April 2008

Various models have been proposed as bivariate forms of the exponential distribution. A brief but comprehensive review is presented which classifies, interrelates and contrasts the different models and outlines what is known about distributional properties, applicability and estimation and testing of parameters (particularly the association parameter). Some new results are presented for one particular model. Maximum likelihood, and moment–type, estimators of the association parameter are examined. Asymptotic variances are derived and attention is given to the relative efficiency of the estimators and to problems of their evaluation.
MULTIPLE FAILURE CAUSES AND OBSERVATIONS OF TIME DEPENDENT COVARIABLES
Authors: Hempenius A.L. , Mulder P.G.H.
Published: April 2008

In this paper firstly a summary of the theory of competing risks is presented; it shows how cause specific failure time distributions, failure probabilities and failure rate functions relate to the joint survivor function in the presence of various competing failure causes. This first part of the paper gives the insight useful for the second part, which concerns the way in which the dependency of the failure process on given time–dependent observations of covariables is specified and estimated. An application is presented briefly.
A NONPARAMETRIC TEST AGAINST ORDERED ALTERNATIVES FOR DATA DEFINED BY INTERVALS
Authors: Abel U.
Published: April 2008

Abstract.The paper deals with a generalization of the Jonckheere test against ordered alternatives which allows for arbitrary censoring. It includes some previously published tests as special cases.
ESTIMATION OF PROBABILITY MODELS FROM INCOME CLASS DATA
Authors: Cramer J.S.
Published: April 2008

Abstract. Many household surveys report income by a limited number of classes only. In Engel curve analyses of such data, income is usually equated to the class midpoint. We argue that it is better to specify a continuous income distribution over the entire range, and to estimate its parameters jointly with the Engel curve coefficients; the position of the dependent variable within income classes is sufficiently informative about the income distribution parameters. The method is illustrated for a simple logit model of automobile ownership. The effect on estimation is perceptible, but not impressive; further analysis suggests that the standard method is acceptable provided some care is taken over the income class limits at the lower end of the range.
RANK TESTS IN 2X2 DESIGNS
Authors: Brunner E. , Neumann N.
Published: April 2008

Abstract. In literature numerous attempts can be found for the evaluation of two factor designs with fixed effects by means of rank tests. The aim of the present article is to show the limits of these methods and to give some new procedures for 2X2 designs. First, functionals of distribution functions shall be defined whose relations to the usual parameters of the linear model are analysed. These functionals are free of nuissance parameters under the respective hypothesis; they are estimated by special ranks of the data. The asymptotic distribution of these statistics is derived by a generalization of the Chemoff–Savage theorem for correlated random variables. The asymptotic variance depends on the parent distribution function but it can be estimated by using special rank methods. Thus, one obtains asymptotically distribution–free tests for two–factor designs with fixed effects. Some counter examples show why it is not possible to construct suitable rank tests for greater designs than the 2X2 design. The paper closes with a discussion of the drawbacks of the well known rank transform.
A note on complete families of distributions
Authors: Oosterhoff J. , Schriever B.F.
Published: April 2008

Some methods to establish completeness of families of distributions are discussed. Several well known parametric families are shown to be complete.
On the construction of multivariate permutation tests in the two–sample case
Authors: van Putten B.
Published: April 2008

This paper is concerned with multivariate generalizations of two–sample rank tests, the bivariate Wilcoxon test in particular.
On Discrete oc–Unimodality
Authors: Abouammoh A.M.
Published: April 2008

A definition of α–unimodality for integer–valued random variables is introduced. Some characterization results in terms of probability mass functions and characteristic functions are established. Properties of generalized discrete uni–modality are investigated. Further, by use of limiting properties, discrete α–unimodality is shown to lead to the concept of α–unimodality for the real–valued random variables due to OLSHEN and SAVAGE (1970).
Approximating the distribution of Greenwood's statistic
Authors: Does R.J.M.M. , Helmers R. , Klaassen C.A.J.
Published: April 2008

Statistics based on uniform spacings are often used in goodness‐of‐fit problems. In this paper special attention is paid to the distribution of Greenwood's statistic. Although its asymptotic distribution is normal, the normal approximation is extremely bad, even for large sample sizes. It is shown that the Edge‐worth expansion yields a considerably better approximation for the distribution of this statistic. Furthermore, an overview is given of the higher order asympto‐tics for the sum of functions of uniform spacings, of which Greenwood's statistic is a special case.
Notes on the Markowitz portfolio selection method
Authors: Kriens J. , van Lieshout J. Th.
Published: April 2008

A proof of the validity of Markowitz's critical line method is given for a more general situation than discussed by Markowitz. Next for the Markowitz case with a positive definite covariance matrix explicit expressions are derived for all efficient portfolios. Using these expressions it can be shown that the critical line in the (μ,α2) plane is a representation of a function which is not necessarily differentiable everywhere.
Polytomous logistic regression
Authors: Engel J.
Published: April 2008

In this paper a review will be given of some methods available for modelling relationships between categorical response variables and explanatory variables. These methods are all classed under the name polytomous logistic regression (PLR). Models for PLR will be presented and compared; model parameters will be tested and estimated by weighted least squares and by likelihood. Usually, software is needed for computation, and available statistical software is reported.

An industrial problem is solved to some extent as an example to illustrate the use of PLR. The paper is concluded by a discussion on the various PLR‐methods and some topics that need a further study are mentioned.
Extended Models for Quantal Response Data
Authors: Morgan B.J.T.
Published: April 2008

There is much current interest in trying to improve the fit of the classical logit and probit models for quantal response data. This is done through transforming the dose scale and/or embedding a classical model in a richer parametric family. This paper provides an historical review of the development of this work, and attempts to make practical recommendations. Much of the work extends directly to the case of logistic regression.
The Logit Model in Economics
Authors: Cramer J.S. , Ridder G.
Published: April 2008

This paper reviews aspects of the application of logit models in economics. We consider some economic models that lead to a simple or a multinomial logit specification. A detailed account is given of the possible specifications of the multinomial model. We stress the relationship between distributional assumptions and functional form assumptions. Some (mis)specification tests with individual data are discussed. Moreover, we present a new test. We also consider grouping of continuously recorded data, and the biases introduced by an inappropriate grouping.
On the independence of integer and fractional parts
Authors: Steutel F.W. , Thiemann J.G.F.
Published: April 2008

We use the independence of the integer and fractional parts of exponentially distributed random variables to obtain expressions for the order statistics from a geometric distribution. As our main result we show that a strong form of this independence characterizes the exponential distribution.
Some rank tests for one–sided many–one comparisons
Authors: Rothe G.
Published: April 2008

We compare some nonparametric tests for the (/+ 1)–sample problem with additive effects under the constraint that in every sample the treatment effect is not less than that in the first sample, i.e. of some control. The behavior of the Pitman efficiency of the respective tests (essentially tests of a Kruskal–Wallis–, Wilcoxon–, Fligner–Wolfe–, Steel–, and Nemenyi–type) is discussed which turns out to depend on the level and power of the tests as well as on the directions, from which the alternative tends to the hypothesis. It will be shown that none of the tests under consideration is uniformly superior to the others.
Local asymptotic normality for randomly censored models with applications to rank tests
Authors: Janssen A.
Published: April 2008

For randomly right censored models we study the asymptotic behaviour of linear (rank) statistics under local alternatives. The results can be used to evaluate the asymptotic power of the corresponding tests. For instance we treat the question how to choose the best scores in order to derive asymptotically optimal (rank) tests under certain alternatives.
Approximate inference in multivariate nonlinear functional relationships
Authors: Linssen H.N. , Hillegers L.T.M.E.
Published: April 2008

An estimation procedure based on estimating equations is presented for the parameters in a multivariate functional relationship model, where all observations are subject to error. The covariance matrix of the observational errors may be parametrized and is allowed to be different for different sets of observations. Estimators are defined for the unknown relation parameters and error parameters.

For linear models (i.e. where the model function is linear in the incidental parameters) the estimators are consistent and asymptotically normal. A consistent expression for the covariance matrix of the estimators is derived. The results are valid for general error distributions.

For nonlinear models the estimators are based on locally linear approximations to the model function. The afore mentioned properties of the estimators are now only approximately valid. The adequacy of the approximate inference, based on asymptotic theory for the linearized model, needs at least informal check. Some examples are given to illustrate the estimation procedure.
Albert's theorem applied to problems of efficiency and MSE superiority
Authors: Bekker P.A. , Neudecker H.
Published: April 2008

Albert's Theorem, which is closely related to general results on Schur complements can be successfully applied to statistical problems.

In the present paper a concise proof for a slightly more general version of the theorem will be given. Two applications on efficiency and a structured overview of results on MSE superiority are then presented. They are the main statistical results of this self–contained paper.
Selection from Logistic populations
Authors: van der Laan P.
Published: April 2008

Assume k(k≥ 2) independent populations π1, π2μk are given. The associated independent random variables Xi,(i= 1,2,…k) are Logistically distributed with unknown means μ1, μ2, μk and equal variances. The goal is to select that population which has the largest mean. The procedure is to select that population which yielded the maximal sample value. Let μ(1)≤μ(2)≤…≤μ(k) denote the ordered means. The probability of correct selection has been determined for the Least Favourable Configuration μ(1)=μ(2)==μ(k – 1)=μ(k)–δ where δ > 0. An exact formula for the probability of correct selection is given.
On the standarized empirical process
Authors: Einmahl J.H.J.
Published: April 2008

In this note a new proof of a theorem of CSAKI (1975, 1982) concerning the almost sure behaviour of the standardized empirical process is established.
Regression Sampling in Statistical Auditing: A Practical Survey and Evaluation
Authors: Kleijnen J.P.C. , Kriens J. , Timmermans H. , van den Wildenberg H.
Published: April 2008

Several confidence intervals for the regression estimator are surveyed. A Monte Carlo experiment, based on the NETER and LOEBBECKE (1975) populations, gives estimated coverages and lengths of the different confidence intervals. One interval is exact under the assumption of multivariate normal distributions; it gives longer intervals (hence better coverages) than the interval based on a popular variance estimator. An interval due to ROBERTS (1970) is much too long. Jackknifing gives robust intervals. Rules of thumb for practitioners are given.
On Regression Sampling in Statistical Auditing: Bad Answers to the Wrong Questions?
Authors: de Vos A.F.
Published: April 2008

This paper criticizes the use of regression in audit samples to obtain confidence intervals for the error rate. Also the methodology to evaluate methods by simulation studies using real–life populations is criticized. This is done from a Bayesian viewpoint, which goes as far as stating that in this type of research the wrong questions are answered. A fundamental discussion on the role of model building, illustrated by the use of models in auditing, forms the centre of the paper.
A latent time–budget model
Authors: de Leeuw J. , van der Heijden P.G.M. , Verboon P.
Published: April 2008

Time–budgets summarize how the time of objects is distributed over a number of categories. Usually they are collected in object by category matrices with the property that rows of this data matrix add up to one. In this paper we discuss a model for the analysis of time–budgets that used this property. The model approximates the observed time–budgets by weighted sums of a number of latent time–budgets. These latent time–budgets determine the behavior of all objects. Special attention is given to the identification of the model. The model is compared with logcontrast principal component analysis.
A note on exchangeability of random variables
Authors: Dean A.M. , Wolfe D.A.
Published: April 2008

A sufficient condition for the induced exchangeability or partial exchangeability of linear functions of exchangeable random variables is presented. The use of this result is illustrated through the establishment of conditional exchangeability for two sets of dependent random variables that are important in constructing conditionally distribution–free test procedures for two distinctly different problems.
A Bayesian learning procedure for the.(s, Q) inventory policy
Authors: Boender C.G.E. , Rinnooy A.H.G.
Published: April 2008

We present an asymptotically optimal Bayesian learning procedure for the (s, Q) inventory policy, for the case when the probability distribution of lead time demand is unknown. This distribution is not required to be a member of a certain family, and the maximal lead time demand is also allowed to be unknown. The algorithm developed for this purpose Is an extension of a standard iterative procedure, which in its original form ‐in spite of claims to the contrary‐might produce solution values that are arbitrarily far away from the optimal one.
On the System Setup and the Scheduling Problem in a Flexible Manufacturing System (FMS)
Authors: Spieksma F.C.R. , Vrieze K. , Oerlemans A.G.
Published: April 2008

In this paper we present a model which unifies several existing models with respect to two phases of the planning process of a Flexible Manufacturing System. These phases are the system setup phase and the scheduling phase and in literature they usually are considered separately. We give a mathematical formulation encompassing both phases. From this formulation several existing approaches can be deduced. We also describe some heuristic methods for our model and present the computational results.
The analysis of unbalanced linear models with variance components
Authors: Engel B.
Published: April 2008

Statistical inference for fixed effects, random effects and components of variance in an unbalanced linear model with variance components will be discussed. Variance components will be estimated by Restricted Maximum Likelihood. Iterative procedures for computing the estimates, such as Fisher scoring and the EM‐algorithm, are described.
Multiple‐dose design and bias‐reducing methods for limiting dilution assays
Authors: Strijbosch L.W.G. , Does R.J.M.M. , Albers W.
Published: April 2008

This paper gives an overview of several (mostly recent) statistical contributions to the theory of Limiting and Serial Dilution Assays (LDA's, SDA's). A simple and useful method is presented for the setup of a design for an LDA or an SDA. This method is based on several user‐supplied design parameters, consisting in the researcher's advance information and other parameters inherent to the particular problem. The commonly used Maximum Likelihood (ML) and Minimum Chi‐square methods for the estimation of the unknown parameter in an LDA or an SDA are described and compared to several bias‐reducing estimation methods, e.g. jackknife and bootstrap versions of the ML method. One particular jackknife version is recommended.
A simple proof of a rate of embedding for the partial sum process
Authors: Shorack G.R.
Published: April 2008

A simple proof of Skorokhod embedding of the partial sum process at a rate is given. Nothing more sophisticated than the HBjek‐RBnyi inequality, the monotone inequality, the one sided reflection principal for Brownian motion and Mill's ratio is used.
Characterizations of logarithmic series distrimtrans
Authors: Kyriakoussis A. , Papageorgiou H.
Published: April 2008

The distributions of X, Y and (X. Y), where X and Y are random variables with probability functions of a logarithmic series law, are characterized by the regression function of X on Y and the conditional distribution of Y given X. Moreover, characterizations are given for binomial or Pascal conditional distributions in terms of the regression function of X on Y and the marginal distribution of X.
Contamination in linear regression models and its influence on estimators
Authors: Boscher H.
Published: April 2008

The consequences of the omission of possibly contaminated observations in a linear regression model for the performance of the ordinary least squares (LS‐) estimator are discussed. We compare the ordinary L Sestimator with the corresponding ‘never pooled’LS‐estimator with respect to the matrix‐valued mean squared error. Necessary and sufficient conditions are derived for the superiority of an estimator to another one and tests are proposed to check these conditions. Finally the resulting preliminary‐test‐estimators are investigated.
Record values of the Lomax distribution
Authors: Ahsanullah M.
Published: April 2008

In this paper, firstly an introduction to the idea of record values for a sequence of independent and identically (Lomax or Pareto II) distributed random variables is given. Some of the distributional properties of these record values and moments up to second order are derived. These moments clearly depend on the location, scale and shape parameter of the Lomax distribution and two types of estlmators of these parameters, based on a series of observed record values are presented.
Shake‐and‐bake algorithms for the identification of nonredundant linear inequalities*
Authors: Romeijn H.E.
Published: April 2008

Two probabilistic shake‐and‐bake algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities. The algorithms proceed by generating a random sequence of points on the boundary of a polyhedron, and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence. The limiting distribution of the sequence of points generated by the algorithms is proven to be uniform on the boundary of the polyhedron.
Regression analysis with dichotomous regressors and misclassification
Authors: Bekker P.A. , van Montfort K. , Mooijaart A.
Published: April 2008

We discuss a regression model in which the regressors are dummy variables. The basic idea is that the observation units can be assigned to some well‐defined combination of treatments, corresponding to the dummy variables. This assignment can not be done without some error, i.e. misclassification can play a role. This situation is analogous to regression with errors in variables. It is well‐known that in these situations identification of the parameters is a prominent problem. We will first show that, in our case, the parameters are not identified by the first two moments but can be identified by the likelihood. Then we analyze two estimators. The first is a moment estimator involving moments up to the third order, and the second is a maximum likelihood estimator calculated with the help of the EM algorithm. Both estimators are evaluated on the basis of a small Monte Carlo experiment.
Robustness of normal theory statistics in structural equation models*
Authors: Mooijaart A. , Bentler P.M.
Published: April 2008

A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.
Some remarks on measurement errors and the identification of panel data models*
Authors: Hsiao C. , Taylor G.
Published: April 2008

We demonstrate that despite the common worry about the possible correlations between the unobserved individual effects and the explanatory variables in panel data models the likelihood approach can provide a unified framework towards the study of the identification of a panel data model subject to measurement errors. In fact, it can also serve as a basis for deriving efficient estimation methods.
Cooperation and conflict among nations: An application of multi‐sample confirmatory factor analysis
Authors: Faber J.
Published: April 2008

The measurement of cooperation and conflict among nations differs greatly among several empirical studies of international relations. In the multidimensional approach to the measurement of both concepts, cooperation and conflict are considered to be unmeasured traits of various indicators in different areas of interest. Insight into the validity of the measurement theory can be gained from the fit of the estimated measurement model and from the estimates of the unknown parameters. These estimates are obtained through confirmatory factor analysis of data on observable policy Indicators of both concepts (see e.g., Jöreskog, 1969). The reliability of the estimated model can be investigated by means of multi‐sample confirmatory factor analysis, which allows one to fit a specified model to several data sets simultaneously. Maximum likelihood estimates of the unknown parameters of one‐sample and multi‐sample confirmatory factor analysis models, based on data available in COPDAB, can be obtained by using the LISREL‐VI program (see Jöreskog and Sörbom (1986). The results indicate that cooperation and conflict in foreign policies of nations have de‐escalating effects upon each other.
Statistical analysis of change in networks
Authors: Frank O.
Published: April 2008

A survey is given of random graphs and random graph processes which can be used to describe and analyze networks that are changing with time. Marko‐vian change over time, log‐linear models for change, and conditionally uniform models for change are described. It is noted that estimation is usually complex if the random graph involves dependent dyads. Models with deterministic change over time may be a way to avoid the difficulties implied by dependent dyads. Logit regression methods are described that can be used to estimate such models.
Asymptotic distributions in random graphs with applications to social networks
Authors: Nowicki K.
Published: April 2008

Various kinds of subgraph counts have been proposed as important statistics in the social sciences: for instance, in connection with studies of the structural properties of social networks. Since the empirical structure in question often involves an element of randomness, subgraph counts are random variables and, consequently, we need to describe their probabilistic properties. In this paper we give a survey of results dealing with the asymptotic distributions of general subgraph counts for a number of standard graph distributions. Although we do not include proofs for all the results, we illustrate the methodology used through studies of asymptotic behaviour for certain subgraph counts.
Approximation for the cumulative and inverse gamma distribution
Authors: Revfeim K.J.A.
Published: April 2008

The gamma distribution function can be expressed in terms of the Normal distribution and density functions with sufficient accuracy for most practical purposes.

The distribution function for the density xΛ‐1e‐x/μ/μΛΓ(A) on 0 <x<∞ is well approximated by e ‐R(Λ){(1 + 1/1 2Λ) φ(z) + 11 ‐z/4Λ1/2+2(z2+ 2)/45Λ] φ(z)/3Λ1/2} where φ(z)≅1/[1 +e‐2z(√2/π+z2 /28)] and φ(z) = e‐z2 /2/√2π are the Normal distribution and density functions, y is the appropriate root of y‐y2/6+y3/36‐y4/270= In (x/Λμ), z=Λ1/2 y, and R(Λ) is the remainder term in Stirling's approximation for In Γ(Λ).
A Statistical analysis of spatial point patterns A case study
Authors: Barendregt L.G. , Rottschäfer M.J.
Published: April 2008

In the project “statistical image analysis” of CWI we have studied some spatial point patterns that originated from biological observations. These observations were the positions of so called EGF‐receptors on the surface of human carcinoma cells.

We propose a stochastic model for these point patterns. Since the EGF‐receptors appear in clusters on the cell surface, we have opted for the Poisson‐cluster‐process as the model. We estimated the three parameters in this process by means of a method described by Diggle. We also did some work in assessing the statistical reliability of our estimates.
On randomization, modeling and experimental design; a new example in an old discussion
Authors: de Vos A.F.
Published: April 2008

Fisher and “Student” quarreled in the early days of statistics about the design of experiments, meant to measure the difference in yield between to breeds of corn. This discussion comes down to randomization versus model building. More than half a century has passed since, but the different views remain. In this paper the discussion is put in terms of artificial randomization and natural randomization, the latter being what remains after appropriate modeling. Also the Bayesian position is discussed. An example in terms of the old corn‐breeding discussion is given, showing that a simple robust model may lead to inference and experimental design that outperforms the inference from randomized experiments by far. Finally similar possibilities are suggested in statistical auditing.
Solution sets for linear dynamic errors‐in‐variables models*
Authors: Scherrer W. , Deistler M. , Kopel M. , Reitgruber W.
Published: April 2008

In the paper solution sets for linear dynamic errors‐in‐variables (or factor‐) models with uncorrelated error components are analysed. Special emphasis is given to the description of the set of all systems compatible with given second moments of the observations for the case of three‐ and four‐ dimensional observations
R2 in Seemingly Unrelated Regression Equations
Authors: Neudecker H. , Windmeijer F.A.G.
Published: April 2008

Some properties are discussed of McElroy's measure of goodness of fit for Zellner's seemingly unrelated regression equations (Mc Elroy, 1977). Amongst them are asymptotic properties. We show that a possible alternative, the squared sample correlation coefficient of the npvector of dependent variables y=(y1′, y2′,…, yg′)′ and the vector of estimated variables y, both premultiplied by the inverse of the square root of the variance matrix of y, is not invariant under changes of location or scale. This measure therefore can't be considered as a serious alternative to McElroy's.
The compactification of generalized linear models
Authors: Verbeek A.
Published: April 2008

The main purpose of this paper is to unify and extend the existing theory of ‘estimated zeroes’ in log‐linear and logit models. To this end it is shown that every generalized linear model (GLM) can be embedded in a larger model with a compact parameter space and a continuous likelihood (a ‘CGLM’). Clearly in a CGLM the maximum likelihood estimate (MLE) always exists, easing a major data analysis problem. In the mean‐value parametrization, the construction of the CGLM is remarkably simple; except in a rather pathological and rare case, the estimated expected values are always finite., In the β‐parametrization however, the compactification is more complex; the MLE need not correspond with a finite β, as is well known for estimated zeros in log‐linear models. The boundary distributions of CGLMs are classified in four categories: ‘Inadmissible’, ‘degenerate’, ‘Chentsov’, and ‘constrained’. For a large class of GLMs, including all GLMs with canonical link functions and probit models, the MLE in the corresponding CGLM exists and is unique. Even stronger, the likelihood has no other local maxima. We give equivalent algebraic and geometric conditions (in the vein of Haberman (1974, 1977) and Albert and Anderson (1984) respectively), necessary for the existence of the MLE in the GLM corresponding to a finite β. For a large class of GLMs these conditions are also sufficient. Even for log‐linear models this seams to be a new result.
A Note on the Estimation of Non‐Differentiable Functions of MuItinomial ProbabiIities
Authors: Weba M.
Published: April 2008

Abstract. Consider the problem of estimating f(θ) where fis a given function and 8 is the unknown parameter of a multinomial distribution. In order to describe the asymptotic behaviour of the frequency substitution estimator, conventional methods typically require differentiability of f, and the error representations depend on the unknown parameter θ.

In this note, a pararneter‐free bound for the mean square error is derived which requires continuity of f only.
On the existence of locally mvu estimators
Authors: Plachky D.
Published: April 2008

It is proved that there exists an unbiased estimator for some real parameter of a class of distributions, which has minimal variance for some fixed distribution among all corresponding unbiased estimators, if and. only if the corresponding minimal variances for all related unbiased estimation problems concerning finite subsets of the underlying family of distributions are bounded. As an application it is shown that there does not exist some unbiased estimator for θk+c(ε≥0) with minimal variance for θ=0 among all corresponding unbiased estimators on the base of k i.i.d. random variables with a Cauchy‐distribution, where θ denotes some location parameter.
Estimating the Weight Undersize Distribution for the Wicksell problem
Authors: Hoogendoorn A.W.
Published: April 2008

In Wicksell's corpuscle problem one is interested in estimating the distribution of sphere diameters from the diameters of circle profiles obtained by a random section of the body containing the sphericle particles. The problem is known to be an ill posed inverse problem. Several regularization techniques have been applied to find solutions. We will review some of these in this article. In practical situations one often is more interested in the distribution of weight rather than the distribution of diameters. In estimating the weight undersite distribution similar problems are encountered. We will consider an estimator that is obtained by smoothing the distribution function of the circle diameters locally. It will be shown how the bandwidth must be chosen to obtain consistency and mean square error optirnality. Also asymptotic normality will be shown.
Descriptive statistics of large data sets by scatter plots, an exploratory approach
Authors: Rey W.J.J.
Published: April 2008

In the analysis of large tables of M variables on N observations one is interested in the relations between the variables and it is usual to inspect the M(M‐1)/2 scatter plots of N points. Clearly, the scatter plot approach relies on visual inspection and is to be preferred in so far as applicable to detect simple relations, namely when M is small. Other approaches are needed for large values of M.

We consider that only the relatively few scatter plots that present a ‘structure’ are of interest for an exploratory analysis and, by ‘structure’, we mean a domain of specially high local density in the plot. Based on this concept, we propose a method constructed around two steps: the selection of the possibly interesting pairs of variables and the validation of the corresponding scatter plots. The selection of the pairs results from an algorithm based on a binary partitioning tree. The validation of the corresponding scatter plots enables the production of only those where a structure is found the recognition of a structure is derived from a statistic based on the length of the Minimum Spanning Tree constructed on the N points of the candidate scatter plot.

For illustration, we report on an industrial application where the method is routinely applied for exploratory purposes.
The analysis of proportions in agricultural experiments by a generalized linear mixed model
Authors: Jansen J. , Hoekstra J. A.
Published: April 2008

This paper is concerned with the statistical analysis of proportions involving extra‐binomial variation. Extra‐binomial variation is inherent to experimental situations where experimental units are subject to some source of variation, e.g. biological or environmental variation. A generalized linear model for proportions does not account for random variation between experimental units. In this paper an extended version of the generalized linear model is discussed with special reference to experiments in agricultural research. In this model it is assumed that both treatment effects and random contributions of plots are part of the linear predictor. The methods are applied to results from two agricultural experiments.
Isotonic estimators of monotone densities and distribution functions: basic facts
Authors: Groeneboom P. , Lopuhaa H. P.
Published: April 2008

We present short proofs of some basic results from isotonic regression theory. A straightforward argument is given to show that the left continuous version of the concave majorant of the empirical distribution function maximizes the likelihood function f↦f(X,)…f(Xn) within the class of non‐increasing densities. Similarly, it is shown that the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of interval censored data has an interpretation in terms of the left derivative of a convex minor ant. Finally, a short proof is given to show that the number of vertices of the concave major ant of the uniform empirical distribution function is asymptotically normal with asymptotic mean and variance both equal to log n.
Estimation of linear models with nequal restrictions
Authors: Moors J. J. A. , van Houwelingen J. C.
Published: April 2008

Inequality constrained regression involves the notion of a truncated parameter space, which was studied extensively by Moors (1985). His general results are extended here and applied to linear models. Using the invariance principle, for every observation x a set Vx is defined with the property that estimators taking values in Vx (with positive probability) are inadmissible. One of the main conclusions is that the usual estimators in inequality constrained regression are inadmissible; a method to obtain better estimators is indicated.
Identification of simultaneous equation models with measurement error: a computerized evaluation
Authors: Merckens A. , Bekker P. A.
Published: April 2008

Rank conditions for identification in structural models are often difficult evaluate. Here we consider simultaneous equation models with measurement error and we show that previously published rank conditions for identification are not well‐suited for evaluation. An alternative rank condition is derived and a computer algebra program is presented that takes care of both the construction and the computation of the rank of the relevant Jacobian matrix. It uses the parameter restrictions as input in order to characterize the identification situation of the individual parameters in the output.
The ascending ladder height distribution for a certain class of dependent random walks
Authors: Asmussen S. , Schmidt V.
Published: April 2008

A random walk {Sn} with Sn= (Xl ‐ Yl) +…+ (Xn ‐ Yn) is considered where the Xn Yn are non‐negative random variables, the Yn are exponentially distributed with rate δ and the Xn have common distribution function B. It is shown that the expression δ(1 ‐ S (x)) for the density of the ascending ladder height distribution of (Sn), which is well‐known for i.i.d. Xn, holds also when the Xn form a stationary sequence of not necessarily independent random variables.
New results in retrial queueing systems with breakdown of the servers
Authors: Artalejo J. R.
Published: April 2008

We consider retrial queues with servers that are subject to active breakdowns. First, we concentrate on Markovian queueing models. For the multiserver case we obtain sufficient conditions for ergodicity. For the singleserver case we introduce new performance measures: the “orbit” idle period and the “orbit” busy period. Further, we investigate the asymptotic behaviour under high intensity of retrials. We also give an algorithm to compute the steady‐state probabilities for theM/G/lretrial queue with breakdowns. The algorithm is based on a regenerative approach.
On the asymptotically uniform distribution modulo 1 of extreme order statistics
Authors: Wilms R. J. G. , Brands J. J. A. M.
Published: April 2008

Let (Xm)∞1 be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of rnax (X1., Xn) to converge in distribution, as n←∞ to a random variable with a uniform distribution on [0, 1).
Goodness of fit in the linear model without a constant term
Authors: Windmeijer F. A. G.
Published: April 2008

Some properties of two goodness‐of‐fit measures are analysed in the case the linear model does not contain a constant term. One measure is proposed by Batten (1987), the other is the squared sample correlation coefficient. In particular, attention is paid to the bias and moments of the measures.