A note on LeCam’s bound for the distance between the Poisson binomial and the Poisson distribution

n possibly different success probabilities p ₁, p ₂, ..., p _n is frequently approximated by a Poisson distribution with parameter λ = p ₁ + p ₂ + ... + p _n . LeCam's bound p ² ₁ + p ² ₂ + ... + p _n ² for the total variation distance between both distributions is particularly useful provided the success probabilities are small. The paper presents an improved version of LeCam's bound if a generalized d-dimensional Poisson binomial distribution is to be approximated by a compound Poisson distribution. Received: May 10, 2000; revised version: January 15, 2001     

Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods

Summary.  Recently several studies have analysed active labour market policies by using a recently proposed matching estimator for multiple programmes. Since there is only very limited practical experience with this estimator, this paper checks its sensitivity with respect to issues that are of practical importance in this kind of evaluation study. The estimator turns out to be fairly robust to several features that concern its implementation. Furthermore, the paper demonstrates that the matching approach per se is no panacea for solving all the problems of evaluation studies, but that its success depends critically on the information that is available in the data. Finally, a comparison with a bootstrap distribution provides some justification for using a simplified approximation of the distribution of the estimator that ignores its sequential nature.     

Analysis of individual- and time-specific covariate effects on survival of Serinus serinus in north-eastern Spain

We developed models for the analysis of recapture data for 2678 serins ( Serinus serinus ) ringed in north-eastern Spain since 1985. We investigated several time- and individual-specific factors as potential predictors of overall mortality and dispersal patterns, and of gender and age differences in these patterns. Time-specific covariates included minimum daily temperature, days below freezing, and abundance of a strong competitor, siskins ( Carduelis spinus ) during winter, and maximum temperature and rainfall during summer. Individual covariates included body mass (i.e. body condition), and wing length (i.e. flying ability), and interactions between body mass and environmental factors. We found little support of a predictive relationship between environmental factors and survival, but good evidence of relationships between body mass and survival, especially for juveniles. Juvenile survival appears to vary in a curvilinear manner with increasing mass, suggesting that there may exist an optimal mass beyond which increases are detrimental. The mass-survival relationship does seem to be influenced by at least one environmental factor, namely the abundance of wintering siskins. When siskins are abundant, increases in body mass appear to relate strongly to increasing survival. When siskin numbers are average or low the relationship is largely reversed, suggesting that the presence of strong competition mitigates the otherwise largely negative aspects of greater body mass. Wing length in juveniles also appears to be related positively to survival, perhaps largely due to the influence of a few unusually large juveniles with adult-like survival. Further work is needed to test these relationships, ideally under experimentation.     

Saddlepoint approximations for some models of circular data

In this article we provide saddlepoint approximations for some important models of circular data. The particularity of these saddlepoint approximations is that they do not require solving the saddlepoint equation iteratively, so their evaluation is immediate. We first give very accurate approximations to P-values, critical values and power functions for some optimal tests regarding the concentration parameter under wrapped symmetric α-stable and circular normal models. Then, we consider an approximation to the distribution of a projection of the two-dimensional Pearson random walk with exponential step sizes.     

Discovering influential cases in linear regression with MINITAB: Peeking into multidimensions with a MINITAB macro

Various diagnostic statistics have been proposed to help identify cases that markedly affect, or influence, the features of a fitted linear regression model. Once influential cases are found, decisions can be made regarding their worth in the model building process. Since a subject data set may contain both singly influential cases and influential multiple case subsets, the capability to assess the joint influence of cases is needed for a complete analysis. The aim of this work is to briefly review Cook’s distance measure for multiple cases, an effective diagnostic for this purpose, and present a method using it to search for influential multiple case subsets. The method is applied in two example analyses by way of a MINITAB Statistical Software macro.     

A Weighted Least Squares Approach to Levene's Test of Homogeneity of Variance

In 1960 Levene suggested a potentially robust test of homogeneity of variance based on an ordinary least squares analysis of variance of the absolute values of mean-based residuals. Levene's test has since been shown to have inflated levels of significance when based on the F-distribution, and tests a hypothesis other than homogeneity of variance when treatments are unequally replicated, but the incorrect formulation is now standard output in several statistical packages. This paper develops a weighted least squares analysis of variance of the absolute values of both mean-based and median-based residuals. It shows how to adjust the residuals so that tests using the F -statistic focus on homogeneity of variance for both balanced and unbalanced designs. It shows how to modify the F -statistics currently produced by statistical packages so that the distribution of the resultant test statistic is closer to an F-distribution than is currently the case. The weighted least squares approach also produces component mean squares that are unbiased irrespective of which variable is used in Levene's test. To complete this aspect of the investigation the paper derives exact second-order moments of the component sums of squares used in the calculation of the mean-based test statistic. It shows that, for large samples, both ordinary and weighted least squares test statistics are equivalent; however they are over-dispersed compared to an F variable.     

Promoting the Visibility of Educational Research through an Institutional Repository

Established in 1994 through the amalgamation of several teacher training colleges, The Hong Kong Institute of Education (HKIEd) is the major multidisciplinary teacher education provider in the Hong Kong SAR. Despite this, the Institute does not have a particularly high research profile when compared with its peer institutions in Hong Kong and around the world. Its research publishing achieves modest exposure and impact in international educational research literature. The Institute has a goal to attain the title of a “university of education” and has identified an improvement in its research output and profile as critical to achieving this. In this context the HKIEd Library embarked on the redevelopment of its institutional repository, changing its direction from being an archive of institutional publications to one which brought together and offered access to the sum total of published output of the Institute since its foundation, in a deliberate effort to promote Institute research. This paper explores the particular approach taken by the Library to the development of the institutional repository, how the repository contributes directly to and aligns with the research strategies of the Institute, and the impact the Repository has had so far on improving the profile of research at HKIEd.     

Statistical consulting at German universities: Results of a survey

The article presents the results of a survey on statistical consulting at German universities, where the survey focused on obtaining information on when, where and to whom statistical consulting is provided. We investigate the financial frame of the activity and question the advantages and disadvantages from a consultant’s point of view.     

The negative binomial–beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial–beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.