Shape-restricted inference for Lorenz curves using duality theory

Darinka Dentcheva and Spiridon Penev

Statistics & Probability Letters, 2010, vol. 80, issue 5-6, 403-412

Abstract: We propose a new methodology for estimating curves under a convexity restriction based on Fenchel duality and wavelet approximations. In contrast to approaches where a possibly non-convex estimator is convexified at a second stage, our procedure allows us to construct directly an estimator with a convex shape. The method is applied to the estimation of the Lorenz curve. Applications to estimation of average value at risk, as well as multivariate generalisations to Lorenz surfaces are mentioned. We show asymptotic efficiency which demonstrates that the convexity is achieved at no extra cost.

Date: 2010
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