Critical objective function values in linear sum assignment problems

The linear sum assignment problem has been well studied in combinatorial optimization. Because of the integrality property, it is a linear programming problem with a variety of efficient algorithms to solve it. In the given research, we present a reformulation of the linear sum assignment problem and a Lagrangian relaxation algorithm for its reformulation. An important characteristic of the new Lagrangian relaxation method is that the optimal Lagrangian multiplier yields a critical bottleneck value. Lagrangian relaxation has only one Lagrangian multiplier, which can only take on a limited number of values, making the search for the optimal multiplier easy. The interpretation of the optimal Lagrangian parameter is that its value is equal to the price that must be paid for all objects in the problem to be assigned.     

Exact Tests of Significance in Higher Dimensional Tables

We describe methods used to provide an exact test of significance of the hypothesis that all factors are mutually independent of each other in 2³ and 2⁴ contingency tables. Several numerical examples demonstrate the advantages of exact tests over approximate significance levels. We give bounds on the number of tables needed to perform this exact significance test. In four or more dimensions the number of tables in this enumeration becomes astronomical with even modest sample sizes. Inverting the characteristic function of the exact distribution has proved useful in these situations.     

Goodness‐of‐fit testing based on a weighted bootstrap: A fast large‐sample alternative to the parametric bootstrap

The process comparing the empirical cumulative distribution function of the sample with a parametric estimate of the cumulative distribution function is known as the empirical process with estimated parameters and has been extensively employed in the literature for goodness‐of‐fit testing. The simplest way to carry out such goodness‐of‐fit tests, especially in a multivariate setting, is to use a parametric bootstrap. Although very easy to implement, the parametric bootstrap can become very computationally expensive as the sample size, the number of parameters, or the dimension of the data increase. An alternative resampling technique based on a fast weighted bootstrap is proposed in this paper, and is studied both theoretically and empirically. The outcome of this work is a generic and computationally efficient multiplier goodness‐of‐fit procedure that can be used as a large‐sample alternative to the parametric bootstrap. In order to approximately determine how large the sample size needs to be for the parametric and weighted bootstraps to have roughly equivalent powers, extensive Monte Carlo experiments are carried out in dimension one, two and three, and for models containing up to nine parameters. The computational gains resulting from the use of the proposed multiplier goodness‐of‐fit procedure are illustrated on trivariate financial data. A by‐product of this work is a fast large‐sample goodness‐of‐fit procedure for the bivariate and trivariate t distribution whose degrees of freedom are fixed. The Canadian Journal of Statistics 40: 480–500; 2012 © 2012 Statistical Society of Canada     

Penalized triograms: total variation regularization for bivariate smoothing

Summary.  Hansen, Kooperberg and Sardy introduced a family of continuous, piecewise linear functions defined over adaptively selected triangulations of the plane as a general approach to statistical modelling of bivariate densities and regression and hazard functions. These triograms enjoy a natural affine equivariance that offers distinct advantages over competing tensor product methods that are more commonly used in statistical applications. Triograms employ basis functions consisting of linear 'tent functions' defined with respect to a triangulation of a given planar domain. As in knot selection for univariate splines, Hansen and colleagues adopted the regression spline approach of Stone. Vertices of the triangulation are introduced or removed sequentially in an effort to balance fidelity to the data and parsimony. We explore a smoothing spline variant of the triogram model based on a roughness penalty adapted to the piecewise linear structure of the triogram model. We show that the roughness penalty proposed may be interpreted as a total variation penalty on the gradient of the fitted function. The methods are illustrated with real and artificial examples, including an application to estimated quantile surfaces of land value in the Chicago metropolitan area.     

Correction to: Comparison of joint control schemes for multivariate normal i.i.d. output

AStA Advances in Statistical Analysis - In the original paper, we incorrectly stated that...     

From Nowhere: Space,Race, and Time in How Young Minority Men Understand Encounters with Gangs

Research on gangs within minority communities often focuses on gang crime and violence, and gang organization. Few studies examine the non-gang member side of the equation, especially in how potential victims make sense of gang encounters. This paper reveals how young Black and Latino men interpret gang encounters, interpretations that differ because of the following: one’s ethnicity, a gang’s ethnicity, the state of interethnic gang conflict, and a space’s ethnic makeup. It will also examine the intersection of time, specifically as to how shifting neighborhood demographics change the perceptions of these young minority men. This research is based on ethnographic fieldwork conducted in both Compton and South Central.     

Involvement and emancipation of the worker. Action research in a university hospital

The present action research article is linked to an ergonomics project in a university hospital. The author's proposal is to focus action on the effective worker involvement required for the creation of spaces/mechanisms within organizations where people can enhance cooperation and deliberation on matters relating to work. For this purpose, a committee was introduced to assist in finding problems and solutions directly in work situations, so that workers could experience relative autonomy allowing them to develop procedures and choose tools appropriate to their own real needs. Based on this organizational implementation and on subsequent interviews, the practical results are analyzed and related to employee involvement. One can conclude that workers in all areas of the organization can be active elements for improving working conditions and productivity in companies.     

The workers role in knowledge management and sustainability policies

Based on the concepts of sustainability and knowledge management, this article seeks to identify points of contact between the two themes through an exploratory study of existing literature. The first objective is to find, in international literature, the largest number of papers jointly related to the theme of knowledge management and sustainability. In these documents, the authors looked at the kind of relationship existing between the two themes and what the benefits introduced in organizations are. Based on an ergonomic point of view, the second objective of this article is to analyze the role of the worker (whether at the strategic or operational level) and his importance in this context. The results demonstrate that there is very little literature that addresses the two themes together. The few papers found, however, can be said to show the many advantages of introducing sustainability policies supported by adequate knowledge management. Very little has been studied with regards to the role of workers, which could be interpreted as meaning that little importance is given to the proactive role they may play. On the other hand, there is a high potential for future research in these areas, based on the high level of consideration of workers in knowledge management and sustainability literature, as well as in literature in the areas of ergonomics and sociology.