Weak Convergence of the Regularization Path in Penalized M‐Estimation

Abstract. We consider a function defined as the pointwise minimization of a doubly index random process. We are interested in the weak convergence of the minimizer in the space of bounded functions. Such convergence results can be applied in the context of penalized M‐estimation, that is, when the random process to minimize is expressed as a goodness‐of‐fit term plus a penalty term multiplied by a penalty weight. This weight is called the regularization parameter and the minimizing function the regularization path. The regularization path can be seen as a collection of estimators indexed by the regularization parameter. We obtain a consistency result and a central limit theorem for the regularization path in a functional sense. Various examples are provided, including the ?¹‐regularization path for general linear models, the ?¹‐ or ?²‐regularization path of the least absolute deviation regression and the Akaike information criterion.     

TEACHING THE PRODUCTION/OPERATIONS MANAGEMENT CORE COURSE: INTEGRATING LOGISTICS PLANNING ACTIVITIES

This paper discusses the benefits of restructuring the introductory undergraduate production and operations management (pom) course to improve its pedagogical effectiveness and to better convey the importance of integrating logistics planning activities. The introduction of a dynamic integrative semester-long case study which involves students in applying pom concepts and tools through a simulation game is reported.     

Interpretation of the strength of relations between variables in log-linear analysis*

L'analyse des tableaux de contingence multidimensionelle ne se résume pas à l'étude des seuils de signification de plusieurs modèles. Le modèle choisi par l'analyse log-linéaire propose qu'un certain nombre d'associations et d'interactions sont significatives. Les coefficients des équations log-linéaires sont cependant difficiles à interpréter. La normalisation des configurations d'associations et d'interactions d'un modèle log-linéaire permet d'obtenir des tableaux réduits où les cellules contiennent des statistiques interprétables comme des probabilités. Ces statistiques sont simples à lire et l'importance des relations dévoiées par le modèle s'interprète aisément.
The analysis of multi-dimensional contingency tables does not stop with significance test. But the estimates of the parameters of the log-linear equations are difficult to interpret. We propose herein that the standardization of the chosen model's associations and interactions configurations be used to interpret the strength of relations between variables. This procedure gives simple criteria to weight the associations and interactions of the chosen model. Collapsed tables are readily available and the statistics given by the standardization procedure are interpretable as probabilities.     

A New Kernel Distribution Function Estimator Based on a Non-parametric Transformation of the Data

Abstract.  A new kernel distribution function (df) estimator based on a non-parametric transformation of the data is proposed. It is shown that the asymptotic bias and mean squared error of the estimator are considerably smaller than that of the standard kernel df estimator. For the practical implementation of the new estimator a data-based choice of the bandwidth is proposed. Two possible areas of application are the non-parametric smoothed bootstrap and survival analysis. In the latter case new estimators for the survival function and the mean residual life function are derived.