Efficient Estimation of Parameters of the Negative Binomial Distribution

In this article we investigate a class of moment-based estimators, called power method estimators, which can be almost as efficient as maximum likelihood estimators and achieve a lower asymptotic variance than the standard zero term method and method of moments estimators. We investigate different methods of implementing the power method in practice and examine the robustness and efficiency of the power method estimators.     

Human Development and National Culture: A Multivariate Exploration

We examine the relationship between different aspects of human development and Hofstede’s six dimensions of national culture. Using multivariate regression and canonical correlation analysis, we show that all the dimensions of national culture except masculinity have a significant impact on human development, and that the overall strength of the association between the two groups of variables is a high positive one. In general, the direction of the influence of the national culture variables on economic growth differs from the manner they influence other variables, which reinforces the fact that economic growth does not always translate into true people-centred development. Furthermore, the national culture dimensions do not explain much of the variation in a number of health indicators.     

Hard‐to‐Solve Bimatrix Games

The Lemke–Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d‐space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke–Howson computations, finding an equilibrium by support enumeration takes on average exponential time.     

Asymptotic distributions of statistics and parameter estimates for mixed Poisson processes

Mixed Poisson processes have been used as natural models for events occurring in continuous or discrete time. Our main result is the derivation of the joint asymptotic distributions of statistics, including parameter estimators, computed in different time intervals from data generated by mixed Poisson processes. These distributions can be used, for example, to test the hypothesis about the adequacy of the mixed Poisson process against data. We provide some simulation results and test the model on actual market research data.     

A Simple Univariate Outlier Identification Procedure Designed for Large Samples

A simple univariate outlier identification procedure is presented for the detection of multiple outliers in large and moderate sized data sets. This procedure is a modification of the well-known boxplot outlier-labeling rule. Critical values are easy to obtain for the large sample case for a variety of useful distributions, including the normal, t, gamma, and Weibull. Simple adjustment formulas and graphs are provided for handling smaller samples. Basic probability properties are obtained mathematically and through simulation. Two data sets illustrate the procedure's application as a simple and effective screening tool for both moderate and large-sized univariate samples.     

Surviving mission drift: How charities can turn dependence on government contract funding to their own advantage

The widespread contracting out to British charities of welfare services previously furnished by the state has resulted in many charities operating in fields well outside those specified by their original missions. Challenges connected with charity mission drift have received a great deal of (mainly negative and critical) attention in the nonprofit practitioner literature in recent years, yet no academic research has been completed into exactly how charities respond managerially and operationally to government‐induced mission drift. This empirical study attempted to fill this important gap in knowledge about charity management through in‐depth case studies of three charities known to have experienced substantial mission drift during the last decade, focusing on the styles and types of approach the organizations had adopted in their dealings with government funding agencies. It emerged that the three charities accepted mission drift as a fact of life. Rather than simply supplying contract services to government bodies, the charities were highly proactive in seeking to initiate, direct, control, and assume overall strategic responsibility for state‐funded activities.     

Deriving Approximations in a Random Effects Model for Multicenter Clinical Trials with Binary Response

The design and analysis of multicenter trials based on a random effects model is well developed for a continuous response, but is less well developed for a binary response. Here we describe a random effects model for a binary response for two treatments and show how maximum likelihood estimates for the unknown treatment difference can be derived using a novel approximation to the likelihood. The suggested approximation is easy to use and seems to be better suited to the problem than the Laplace approximation and the approximation based on adaptive Gaussian quadratures. We also derive an approximation for the Fisher information matrix of the treatment parameters. The results extend those previously reviewed by Agresti and Hartzel (2000 Agresti , A. , Hartzel , J. ( 2000 ). Strategies for comparing treatments on a binary response with multi-centre data . Statist. Med. 19 : 1115 – 1139 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]).