A Simple Proof of the Equivalence of the Limiting Distributions of the Continuous-Time and the Embedded Process of the Queue Size in the M/G/1 Queue*

This paper presents an extremely simple proof of the known remarkable fact that for the M/G/1 queue the continuous-time process describing the number of customers in the system has the same limiting distribution as the embedded process describing the number of customers in the system just after service completion epochs.     

An approximation to the limit distribution of the epps-pulley test statistic for normality

Summary The approach of Epps and Pulley (1983) based on the empirical characteristic function is one of the most powerful tools for detecting any departures from normality. We obtain the first four moments of the limiting null distribution of the Epps-Pulley Statistic. Johnson- and Pearson curve fitting yields excellent approximations to simulated quantiles, and by modifying the test statistic the procedure may be carried out easily without the use of extensive tables for all sample sizes. Research done while the author was on leave at the University of Gie?en.     

Research productivity patterns in the organizational behavior and human resource management literature

Closely following the analysis approach used for similar studies in the economics and finance literature, we present the first study to examine if there exists an empirical regularity in the bibliometric patterns of research productivity in the organizational behavior (OB) and human resource management (HRM) literature. Our results present strong evidence that there indeed exists a distinct empirical regularity. It is the so-called Generalized Lotka's Law of scientific productivity pattern: The number of authors publishing n papers is about 1/n^c of those publishing one paper. The observed pattern in the OB and HRM area is interestingly very consistent with those in much older, related business disciplines.     

Anomalies in the Foundations of Ridge Regression

Errors persist in ridge regression, its foundations, and its usage, as set forth in Hoerl & Kennard (1970) and elsewhere. Ridge estimators need not be minimizing, nor a prospective ridge parameter be admissible. Conventional estimators are not LaGrange's solutions constrained to fixed lengths, as claimed, since such solutions are singular. Of a massive literature on estimation, prediction, cross–validation, choice of ridge parameter, and related issues, little emanates from constrained optimization to include inequality constraints. The problem traces to a misapplication of LaGrange's Principle, unrecognized singularities, and misplaced links between constraints and ridge parameters. Alternative principles, based on condition numbers, are seen to validate both conventional ridge and surrogate ridge regression to be defined. Numerical studies illustrate that ridge regression as practiced often exhibits pathologies it is intended to redress.     

Designs for estimating an extremal point of quadratic regression models in a hyperball

This paper is devoted to studying optimal designs for estimating an extremal point of a multivariate quadratic regression model in the unit hyperball. The problem of estimating an extremal point is reduced to that of estimating certain parameters of a corresponding nonlinear (in parameters) regression model. For this reduced problem truncated locally D-optimal designs are found in an explicit form. The result is a generalization of the results of Fedorov and Müller (1997) for onedimensional quadratic regression function in the unit segment. Received February 2002     

Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model

The truncated Poisson regression model is used to arrive at point and interval estimates of the size of two offender populations, i.e. drunk drivers and persons who illegally possess firearms. The dependent capture–recapture variables are constructed from Dutch police records and are counts of individual arrests for both violations. The population size estimates are derived assuming that each count is a realization of a Poisson distribution, and that the Poisson parameters are related to covariates through the truncated Poisson regression model. These assumptions are discussed in detail, and the tenability of the second assumption is assessed by evaluating the marginal residuals and performing tests on overdispersion. For the firearms example, the second assumption seems to hold well, but for the drunk drivers example there is some overdispersion. It is concluded that the method is useful, provided it is used with care.     

A unified approach to bivariate discrete distributions

Here we introduce a bivariate generalized hypergeometric factorial moment distribution (BGHFMD) through its probability generating function (p.g.f.) whose marginal distributions are the generalized hypergeometric factorial moment distributions introduced by Kemp and Kemp (Bull Int Stat Inst 43:336–338,1969). Well-known bivariate versions of distributions such as binomial, negative binomial and Poisson are special cases of this distribution. A genesis of the distribution and explicit closed form expressions for the probability mass function of the BGHFMD, its factorial moments and the p.g.f.’s of its conditional distributions are derived here. Certain recurrence relations for probabilities, moments and factorial moments of the bivariate distribution are also established.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 2

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. We consider case 2, with two observation times for each unobservable event time, in the situation that the observation times cannot become arbitrarily close to each other. It is proved that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

Conditioning as disintegration

Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon–Nikodym derivatives, although we all secretly perform heuristic calculations using elementary definitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information.
One way to engage in rigorous, guilt-free manipulation of conditional distributions is to treat them as disintegrating measures—families of probability measures concentrating on the level sets of a conditioning statistic. In this paper we present a little theory and a range of examples—from EM algorithms and the Neyman factorization, through Bayes theory and marginalization paradoxes—to suggest that disintegrations have both intuitive appeal and the rigor needed for many problems in mathematical statistics.     

Estimation of the scale matrix of a multivariate t-model under entropy loss

This paper deals with the estimation of the scale matrix of a multivariatet-model with unknown location vector and scale matrix to improve upon the usual estimators based on the sample sum of product matrix. The well-known results of the estimation of the scale matrix of the multivariate normal model under the assumption of entropy loss function have been generalized to that of a multivariatet-model. The paper is based on the first author’s unpublished Ph.D. dissertation ‘Estimation of the Scale Matrix of a Multivariate T-model’, University of Western Ontario, Canada. Present address: School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia.