Thinning operations for modeling time series of counts—a survey

The analysis of time series of counts is an emerging field of science. To obtain an ARMA-like autocorrelation structure, many models make use of thinning operations to adapt the ARMA recursion to the integer-valued case. Most popular among these probabilistic operations is the concept of binomial thinning, leading to the class of INARMA models. These models are proved to be useful, especially for processes of Poisson counts, but may lead to difficulties in the case of different count distributions. Therefore, several alternative thinning concepts have been developed. This article reviews such thinning operations and shows how they are successfully applied to define integer-valued ARMA models.     

Probability and statistics: A tale of two worlds?

This comparative study of research productivity and publication habits in probability and statistics completes the paper that was published in this Journal at the end of 1997. It is based on a ten-year survey of eighteen international journals, half of which are specialized in probability theory and the other half in statistics. Paper, author and adjusted page counts yield cursory measures of productivity for countries and institutions that contributed to fundamental research in these two related fields during the period 1986-1995. These data also reveal significant cultural differences between probabilists and statisticians in the volume of research, the length of papers, coauthorship practices, etc. Canada is seen to be one of the strongest contributors to the development of these two disciplines.     

Shape analysis for automated sulcal classification and parcellation of MRI data

We describe geometric invariants that characterize the shape of curves and surfaces in 3D space: curvature, Gauss integrals and moments. We apply these invariants to neuroimaging data to determine if they have application for automatically classifying and parcellating cortical data. The curves of sulci and gyri on the cortical surface can be obtained by reconstructing cortical surface representations of the human brain from magnetic resonance imaging (MRI) data. We reconstructed gray matter surfaces for 15 subjects, traced 10 sulcal curves on each surface and computed geometric invariants for each curve. These geometric features were used classify the curves into sulcal and hemispheric classes. The best classification results were obtained when moment-based features were computed on the sulcal curves in native space. Gauss integral measures showed that they were useful for differentiating the hemispheric location of a single sulcus. These promising results may indicate that moment invariants are useful for characterizing shape on a global scale. Gauss integral invariants are potentially useful measures for characterizing cortical shape on a local, rather than global scale. Gauss integrals have found biological significance in characterizing proteins so it is worthwhile to consider their possible application to neuroscientific data.     

The Joy of Copulas: Bivariate Distributions with Uniform Marginals

We describe a class of bivariate distributions whose marginals are uniform on the unit interval. Such distributions are often called “copulas.” The particular copulas we present are especially well suited for use in undergraduate mathematical statistics courses, as many of their basic properties can be derived using elementary calculus. In particular, we show how these copulas can be used to illustrate the existence of distributions with singular components and to give a geometric interpretation to Kendall's tau.     

Working Life Expectancy at Age 50 in the United States and the Impact of the Great Recession

A key concern about population aging is the decline in the size of the economically active population. Working longer is a potential remedy. However, little is known about the length of working life and how it relates to macroeconomic conditions. We use the U.S. Health and Retirement Study for 1992–2011 and multistate life tables to analyze working life expectancy at age 50 and study the impact of the Great Recession in 2007–2009. Despite declines of one to two years following the recession, in 2008–2011, American men aged 50 still spent 13 years, or two-fifths of their remaining life, working; American women of the same age spent 11 years, or one-third of their remaining life, in employment. Although educational differences in working life expectancy have been stable since the mid-1990s, racial differences started changing after the onset of the Great Recession. Our results show that although Americans generally work longer than people in other countries, considerable subpopulation heterogeneity exists. We also find that the time trends are fluctuating, which may prove troublesome as the population ages. Policies targeting the weakest performing groups may be needed to increase the total population trends.     

Relational commitments in employee–supervisor dyads and employee job performance

We investigated employee commitment to the supervisor and supervisor commitment to the employee within employee–supervisor dyads. We examined the relationships among four commitment mindsets (affective, normative, continuance-sacrifices, and continuance-alternatives) across members of the dyads and their relationships to employee job performance. Using a sample of 300 employee–supervisor dyads from health care organizations, HLM analyses revealed that supervisor positive commitments (i.e., affective, normative, continuance-sacrifices) generally related significantly to employee positive commitments. Moreover, supervisor commitment moderated the relationship of employee affective commitment to job performance, such that when supervisor affective, normative, and continuance-sacrifices commitments were high, the relationship between employee affective commitment and performance was weaker. We discuss the implications of these findings for the understanding of employee–supervisor relationships.