La médiane simpliciale d'Oja: Existence,unicité et stabilité

Oja (1983) examined various ways of measuring location, scatter, skewness, and kurtosis for multivariate distributions. Among other measures of location, he introduced a generalised median known in this paper under the name of the Oja median. In our study of the existence of that median, we show that Oja's definition can only be applied to distributions having a mean. In dimension d θ 2, we establish that the usual method of extension breaks down, which raises the question of the validity of the concept as a notion of median. Two fundamental theoretical properties of that median are also considered: uniqueness and consistency.     

A combined mixed-s-skip sampling strategy to reduce the effect of autocorrelation on the X̄ scheme with and without measurement errors

In order to reduce the effect of autocorrelation on the X¯ monitoring scheme, a new sampling strategy is proposed to form rational subgroup samples of size n. It requires sampling to be done such that: (i) observations from two consecutive samples are merged, and (ii) some consecutive observations are skipped before sampling. This technique which is a generalized version of the mixed samples strategy is shown to yield a better reduction of the negative effect of autocorrelation when monitoring the mean of processes with and without measurement errors. For processes subjected to a combined effect of autocorrelation and measurement errors, the proposed sampling technique, together with multiple measurement strategy, yields an uniformly better zero-state run-length performance than its two main existing competitors for any autocorrelation level. However, in steady-state mode, it yields the best performance only when the monitoring process is subject to a high level of autocorrelation, for any given level of measurement errors. A real life example is used to illustrate the implementation of the proposed sampling strategy.KEYWORDS: Autocorrelation, measurement errors, mixed samples strategy, multiple measurements, skipping sampling strategy, steady-state, zero-state     

The Global Wave of Refugees and Migrants: Complex Challenges for European Policy Makers

This article reviews the burdensome problem posed by the arrival in the European countries of large number of refugees and migrants from countries at war or with little economic opportunities. It differentiates the issues of migrants (for economic reasons) and refugees (humanitarian grounds). This wave of refugees currently poses huge challenges to European policy makers. The article suggests some policy initiatives that could solve or at least control the present chaos, disorder, and uncertainty created by the arrival of this unprecedented number of refugees.     

Mixing and Matching the Green and Gold Roads to Open Access—Take 2

Three years ago, the Gold and Green Roads to Open Access were viewed as complementary strategies, with repositories having the potential of gradually behaving more like journals, and vice versa. Since then, repositories and journals have been progressing on parallel tracks. Re-examining the situation, the reasoning suggested in 2004 appears still valid. Simultaneously, a knowledge economy has made of science a strategic resource. The developing world is essentially invited to contribute to world science with little or no regard to the development of an autonomous scientific capacity. Open Access, in this context, takes a new meaning with one objective to help development of local and autonomous scientific capacity. However, to do so, mixing and matching repositories with journals is needed. Brazil exemplifies this type of development and shows how the Green and Gold roads can mix and match.     

Urban environment, spatial fragmentation and social segration in Latin America: Where does innovation lie?

To “review the urban question” in terms of sustainable development, the premise is formulated that improving infrastructures, equipment and services to preserve the natural and built urban environment is costly and generates expenses of all kinds—at economic and social levels. Without the introduction of equalisation mechanisms, these expenses will increase inequalities between different parts of the urban population.As confirmed by 2 Latin American case studies in Buenos Aires, Argentina, and La Paz Bolivia, the quality of urban environment depends directly on improving living conditions for the resident population. The aim is to assist the poor in developing a rubbish disposal service for the families living in the informal settlements of La Paz, or to extend water supply to the poorer areas on the outskirts of Buenos Aires. The collective benefits of these “innovations” are self-evident. However, understanding the environmental issues involved, and evaluating the social impact of these innovations, means examining what motivates their implementation.The first difficulty was in finding financial and economic information on the global cost of the new technologies, due to the lack of managerial culture and the discretional attitude of private enterprises and public administration.A second observation is that the social dimension of the environmental upgrading process in Latin America cities has been neglected by the main urban decision-makers. In all the contexts, the evolution of the projects’ implementation clearly demonstrates that social issues cannot be dissociated from political ones. Although the players themselves often find it difficult to estimate economic costs, these are nonetheless real and represent burdens that should be distributed equitably among the beneficiaries of services; but which are, in practice, often viewed in terms of profit. This leads to conflicts between different population groups, the political authorities and private intermediaries.Rather than viewing technological action as an unique “source” of innovation, we must consider its global dimension via the social practices it generates. On the other hand, we should reposition every specific event in its immediate environment and see how it reflects contemporary macro-social processes, in a world of “globalisation”.     

A supportive application of management science to marketing strategy formulation

Traditional applications of management science aiming at solving specific decision-making problems are claimed to be often of an aggressive nature. They represent an intrusion into the life space of the managers who are supposed to use them and in many cases are consequently rejected. In the light of the evolution of marketing and corporate modelling over the last twenty years, the authors propose a new supportive approach for management science applications which is user-oriented rather than task-oriented. The characteristics of the aggressive and supportive approaches are contrasted, and an example of a supportive management science application for marketing strategy formulation is described.     

Calculation of the Prokhorov distance by optimal quantization and maximum flow

Calculating exact values of the Prokhorov metric for the set of probability distributions on a metric space is a challenging problem. In this paper probability distributions are approximated by finite-support distributions through optimal or quasi-optimal quantization, in such a way that exact calculation of the Prokhorov distance between a distribution and a quantizer can be performed. The exact value of the Prokhorov distance between two quantizers is obtained by solving an optimization problem through the Simplex method. This last value is used to approximate the Prokhorov distance between the two initial distributions, and the accuracy of the approximation is measured. We illustrate the method on various univariate and bivariate probability distributions. Approximation of bivariate standard normal distributions by quasi-optimal quantizers is also considered.     

Multivariate trimmed means based on the Tukey depth

In univariate statistics, the trimmed mean has long been regarded as a robust and efficient alternative to the sample mean. A multivariate analogue calls for a notion of trimmed region around the center of the sample. Using Tukey's depth to achieve this goal, this paper investigates two types of multivariate trimmed means obtained by averaging over the trimmed region in two different ways. For both trimmed means, conditions ensuring asymptotic normality are obtained; in this respect, one of the main features of the paper is the systematic use of Hadamard derivatives and empirical processes methods to derive the central limit theorems. Asymptotic efficiency relative to the sample mean as well as breakdown point are also studied. The results provide convincing evidence that these location estimators have nice asymptotic behavior and possess highly desirable finite-sample robustness properties; furthermore, relative to the sample mean, both of them can in some situations be highly efficient for dimensions between 2 and 10.