Finite mixtures of multivariate skew t-distributions: some recent and new results

Finite mixtures of multivariate skew t (MST) distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour. Recently, they have been exploited as an effective tool for modelling flow cytometric data. A number of algorithms for the computation of the maximum likelihood (ML) estimates for the model parameters of mixtures of MST distributions have been put forward in recent years. These implementations use various characterizations of the MST distribution, which are similar but not identical. While exact implementation of the expectation-maximization (EM) algorithm can be achieved for ‘restricted’ characterizations of the component skew t-distributions, Monte Carlo (MC) methods have been used to fit the ‘unrestricted’ models. In this paper, we review several recent fitting algorithms for finite mixtures of multivariate skew t-distributions, at the same time clarifying some of the connections between the various existing proposals. In particular, recent results have shown that the EM algorithm can be implemented exactly for faster computation of ML estimates for mixtures with unrestricted MST components. The gain in computational time is effected by noting that the semi-infinite integrals on the E-step of the EM algorithm can be put in the form of moments of the truncated multivariate non-central t-distribution, similar to the restricted case, which subsequently can be expressed in terms of the non-truncated form of the central t-distribution function for which fast algorithms are available. We present comparisons to illustrate the relative performance of the restricted and unrestricted models, and demonstrate the usefulness of the recently proposed methodology for the unrestricted MST mixture, by some applications to three real datasets.     

Age discrimination and working life: Perspectives and contestations – a review of the contemporary literature

This review highlights some of the principal issues and debates surrounding age discrimination at the workplace. Essentially, the existing research in this area can be divided into three broad, although somewhat overlapping, categories. The first explores the underlying causes and consequences of age discrimination at the workplace from one or other theoretical tradition. The second broad body of literature encompasses empirical studies which document the nature and extent of age discrimination, based on the use of official statistics, and/or firm‐level survey evidence. The third explores the effects of various governmental initiatives to reduce the incidence of age discrimination and policy options in this area. Even though age discrimination is widely accepted to be prevalent, its causes are rather more contentious. Age discrimination has variously been ascribed to market imperfections, the product of rational choices and the effects of long‐term changes in the nature of the economy. Policy interventions may be prompted by economic pressure, demographic changes or cultural shifts, and have involved voluntary codes as well as legislation. Although voluntary codes have generally proved ineffective, the literature indicates that more formal regulations may still have only limited efficacy, underscoring the deeply rooted nature of age discrimination in society.     

The Siable-Law Model of Stock Returns

This study investigates the tail shapes of empirical distributions of returns on an extensive group of common stocks. The tails of the return distributions are found to be thinner than those of infinite variance stable distributions. Therefore, although homogeneity is evident in general, economic and statistical inferences drawn from stable-law parameters estimated from samples of stock returns may be misleading. This is in spite of the apparent overall similarity (in shape) between empirical and stable distributions.     

SHORT REVIEWS

Books reviewed in this article: Orley Ashenfelter And David Card (Eds.), Handbook of Labor Economics, Volume 3 Paul Boyle, Keith Halfacree, and Vaughan Robinson, Exploring Contemporary Migration Weixing Chen, The Political Economy of Rural Development in China, 1978–1999 David A. Crocker and Toby Linden (Eds.), Ethics of Consumption: The Good Life, Justice, and Global Stewardship James Z. Lee and Wang Feng, One Quarter of Humanity: Malthusian Mythology and Chinese Realities, 1700–2000 Jonathan M. Mann and Daniel J. M. Tarantola (Eds.), AIDS in the World II: Global Dimensions, Social Roots, and Responses Julian L. Simon, The Economic Consequences of Immigration, Second Edition Sopemi, Trends in International Migration: Continuous Reporting System on Migration. Annual Report, 1999 Edition Jacqueline Stevens, Reproducing the State United Nations Development Programme China, The China Human Development Report United Nations, Economic Commission For Europe, Economic Survey of Europe 1999, No. 1 Kathleen S. Uno, Passages to Modernity: Motherhood, Childhood, and Social Reform in Early Twentieth Century Japan     

A Heart to Learn and Care? Teachers' responses toward special needs children in mainstream schools in Hong Kong

This article examines the problems associated with introducing integrated education into Hong Kong's mainstream schooling system. The research objectives were to examine the experience of teachers in teaching children with special needs in mainstream schools; to examine the attitude of mainstream teachers towards integrated education, and explore whether the differences in perception of difficulties and attitudes are attributable to types of disability and availability of resources. This was achieved through a research strategy utilising a questionnaire survey combined with individual and group interviews. The results demonstrate that there is a clear hierarchy of preference amongst teachers in relation to special needs children. Students with a learning disability and/or behavioural problems pose more challenges to teachers than those with a physical difficulty. Teachers that had both types of special needs children in a class experience more problems in maintaining classroom discipline, have a greater workload and struggle to manage the disparate academic standards amongst students. Teachers in schools with extra funding provisions, teachers trained to teach special needs children, additional counselling resources and specialist support expressed more accepting attitudes towards children with special needs and their admission into mainstream schools. Resource classes did not exert a positive effect on acceptance. More than 70% of questionnaire respondents were supportive of two positive value statements 'realisation of equal opportunities' and 'a good chance for students to interact'. At the same time teachers tended to agree with the statements 'integration was a burden to the schools and teachers' (over 60%) and 'a painful struggle for special students' (48%). Although there is a general normative acceptance of inclusion, the statistical pattern suggests that teachers' attitudes are not static or based solely on ideology.