A weighted spatial median for clustered data

A weighted spatial median is proposed for the multivariate one-sample location problem with clustered data. Its limiting distribution is derived under mild conditions (no moment assumptions) and it is shown to be multivariate normal. Asymptotic as well as finite sample efficiencies and breakdown properties are considered, and the theoretical results are supplied with illustrative examples. It turns out that there is a potential for meaningful gains in estimation efficiency: the weighted spatial median has superior efficiency to the unweighted spatial median particularly when the cluster sizes are widely disparate and in the presence of strong intracluster correlation. The unweighted spatial median for clustered data was considered earlier by Nevalainen et al. (Can J Statist, in press, 2007). The proposed weighted estimators provide companion estimates to the weighted affine invariant sign test proposed recently by Larocque et al. (Biometrika, in press, 2007). An affine equivariant weighted spatial median is discussed in parallel.     

On the geometry of multivariate L 1 objective functions

Summary: Two multivariate L ₁ objective functions, namely the k–variate extensions of the classical mean deviation and mean difference, are considered. The duality between the original data vectors and the hyperplanes going through the origin and k – 1 data points is discussed and, consequently, different interesting representations and interpretations of the multivariate mean deviation are introduced. A similar duality is found between the lift data vectors and the hyperplanes going through k data points leading to different representations of the multivariate mean difference. The objective functions are also shown to have interpretations in terms of the centers of facets of the data based zonotopes and lift zonotopes. Moreover, interchanging the roles of the data vectors and the data hyperplanes yields nonparametric measures of (angular) distances between the data vectors as well as between the hyperplanes. Finally, multivariate sign and rank based tests and estimates in the one–sample and several–samples multivariate cases are discussed to illustrate the theory.*The authors wish to thank the referees for valuable comments and suggestions. The research was partially supported by the Academy of Finland.     

Social Work with Immigrants and Refugees: Developing a Participation-based Framework for Anti-Oppressive Practice

Summary This Research Note represents the first in a two part series,dealing with the experience of social work with immigrants andrefugees in Finland. In this part, the author identifies keyideas and outlines research findings in the major area of employment,including a discussion of the skills and abilities which socialworkers need and can contribute in this area. The next issueof the Journal will present research evidence in relation toa range of community and cultural questions which arise fromthis work, concluding with further discussion of successfulsocial work in this field.     

Immigrant integration in the welfare state: Social work's growing arena

This article examines social work with immigrants in the welfare state context. The work is informed by two previous studies on immigrant and refugee integration in Finland and Canada. Taking a holistic perspective on resettlement, social work can be seen as a crucial support and bridging service through transition. Tasks involve active fostering of linkage to promote immigrant participation in the wider society, a mandate that goes beyond that of guaranteeing access to welfare benefits. The thrusts of empowerment for full participation and effective practice of citizenship include capacity building, networking of resources and fighting discriminatory barriers. Resettlement social work has a singular interest in reexamining the State-third sector and professional-paraprofessional divide. It would be to the advantage of the field to broaden the body of official stakeholders and actors, in the context of new partnerships. The immigrant communities hold needed stocks of cultural competence and resettlement experience, which complement areas of professional expertise. Collaborative partnerships could offer social work the possibility to access community-based resources and to reach needs and problems that may otherwise elude the mainstream social work system in the welfare state.     

Voting paradoxes and referenda

In representational democracies the referenda constitute an additional way for the voters to express their opinions. At the same time they are accompanied by problems of agenda manipulation and interpretation of results. In this context various voting paradoxes and their interrelationships are of considerable interest. In this article particular attention is paid to opinion aggregation paradoxes in referendum institutions. The limits and interrelationships of paradoxes are discussed. Some ways of avoiding paradoxical situations are also outlined. Received: 11 September 1995 / Accepted: 7 January 1997     

One-sample location tests for multilevel data

In this paper, we consider testing the location parameter with multilevel (or hierarchical) data. A general family of weighted test statistics is introduced. This family includes extensions to the case of multilevel data of familiar procedures like the t, the sign and the Wilcoxon signed-rank tests. Under mild assumptions, the test statistics have a null limiting normal distribution which facilitates their use. An investigation of the relative merits of selected members of the family of tests is achieved theoretically by deriving their asymptotic relative efficiency (ARE) and empirically via a simulation study. It is shown that the performance of a test depends on the clusters configurations and on the intracluster correlations. Explicit formulas for optimal weights and a discussion of the impact of omitting a level are provided for 2 and 3-level data. It is shown that using appropriate weights can greatly improve the performance of the tests. Finally, the use of the new tests is illustrated with a real data example.