Inference in model-based cluster analysis

A new approach to cluster analysis has been introduced based on parsimonious geometric modelling of the within-group covariance matrices in a mixture of multivariate normal distributions, using hierarchical agglomeration and iterative relocation. It works well and is widely used via the MCLUST software available in S-PLUS and StatLib. However, it has several limitations: there is no assessment of the uncertainty about the classification, the partition can be suboptimal, parameter estimates are biased, the shape matrix has to be specified by the user, prior group probabilities are assumed to be equal, the method for choosing the number of groups is based on a crude approximation, and no formal way of choosing between the various possible models is included. Here, we propose a new approach which overcomes all these difficulties. It consists of exact Bayesian inference via Gibbs sampling, and the calculation of Bayes factors (for choosing the model and the number of groups) from the output using the Laplace–Metropolis estimator. It works well in several real and simulated examples.     

Exponential inequalities in linear calibration problem

ABSTRACT

Calibration, also called inverse regression, is a classical problem which appears often in a regression setup under fixed design. The aim of this article is to propose a stochastic method which gives an estimated solution for a linear calibration problem. We establish exponential inequalities of Bernstein–Frechet type for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so-mentioned exact solution. To check the validity of our results, a numerical example is proposed.     

Time Preferences and Job Search: Evidence from France

Abstract. Increasing impatience reduces search efforts of unemployed job seekers and therefore decreases the exit rate from unemployment. Also, impatience reduces reservation wage and increases the exit rate. To determine the overall effect of impatience on the exit rate from unemployment, we distinguish between exponential and hyperbolic time preferences. Search effort dominates the reservation wage and decreases the exit rate from unemployment if individuals have hyperbolic, rather than exponential, preferences. Using the French sample of the European Household Panel Survey, we found that search effort has a strong effect on the duration of unemployment, whereas the reservation wage is not significant. This result shows that the job seekers have hyperbolic preferences. Hyperbolic preferences affect problems associated with job search and policies aimed at reducing unemployment.