In frontier analysis, most of the nonparametric approaches (FDH,DEA) are based on envelopment ideas and their statistical theory is now mostly available. However, by construction, they are very sensitive to outliers. Recently, a robust nonparametric estimator has been suggested by Cazals, Florens and Simar (2002). In place of estimating the full frontier, they propose rather to estimate an expected frontier of order m. Similarly, we construct a new nonparametric estimator of the efficient frontier. It is based on conditional quantiles of an appropriate distribution associated with the production process. We show how these quantiles are interesting in efficiency analysis. We provide the statistical theory of the obtained estimators. We illustrate with some simulated examples and a frontier analysis of French post offices, showing the advantage of our estimators compared with the estimators of the expected maximal output frontiers of order m.

This article concerns the analysis of multivariate response data with multivariate regressors. Methods for reducing the dimensionality of response variables are developed, with the goal of preserving as much regression information as possible. We note parallels between this goal and the goal of sliced inverse regression, which intends to reduce the regressor dimension in a univariate regression while preserving as much regression information as possible. A detailed discussion is given for the case where the response is a curve measured at xed points. The problem in this setting is to select basis functions for tting an aggregate of curves. We propose that instead of focusing on goodness of t, attention should be shifted to the problem of explaining the variation of the curves in terms of the regressor variables. A data-adaptive basis searching method based on dimension reduction theory is proposed. Simulation results and an application to a climatology problem are given.

Abstract. Unemployment rates vary widely at the sub-regional level. We seek to explain why such variation occurs, using data for 174 districts in the Midi-Pyrénées region of France for 1990-1991. A set of explanatory variables is derived from theory and the voluminous literature. The best model includes a correction for spatially autocorrelated errors. Unemployment rates are higher in urban areas and, where per capita income is higher, are consistent with the view that unemployment differences largely reflect variations in "amenities." Along with a lack of evidence of housing market rigidities, these suggest that subregional variations in unemployment are not mainly the result of labor market disequilibrium.JEL classification: J60, J64, R12, R23

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