Shape-restricted inference for Lorenz curves using duality theory

Darinka Dentcheva, Spiridon Penev

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish
Pages (from-to)403-412
Number of pages10
JournalStatistics and Probability Letters
Volume80
Issue number5-6
DOIs
StatePublished - 2010

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