Nadaraya’s Estimates for Large Quantiles and Free Disposal Support Curves

Abdelaati Daouia (), Laurent Gardes () and Stéphane Girard ()
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Abdelaati Daouia: University of Toulouse, Toulouse School of Economics (GREMAQ)
Laurent Gardes: Team Mistis, INRIA Rhône-Alpes and Laboratoire Jean Kuntzmann
Stéphane Girard: Team Mistis, INRIA Rhône-Alpes and Laboratoire Jean Kuntzmann

Chapter Chapter 1 in Exploring Research Frontiers in Contemporary Statistics and Econometrics, 2011, pp 1-22 from Springer

Abstract: Abstract A new characterization of partial boundaries of a free disposal multivariate support, lying near the true support curve, is introduced by making use of large quantiles of a simple transformation of the underlying multivariate distribution. Pointwise empirical and smoothed estimators of the full and partial support curves are built as extreme sample and smoothed quantiles. The extreme-value theory holds then automatically for the empirical frontiers and we show that some fundamental properties of extreme order statistics carry over to Nadaraya’s estimates of upper quantile-based frontiers. The benefits of the new class of partial boundaries are illustrated through simulated examples and a real data set, and both empirical and smoothed estimates are compared via Monte Carlo experiments. When the transformed distribution is attracted to the Weibull extreme-value type distribution, the smoothed estimator of the full frontier outperforms frankly the sample estimator in terms of both bias and Mean-Squared Error, under optimal bandwidth. In this domain of attraction, Nadaraya’s estimates of extreme quantiles might be superior to the sample versions in terms of MSE although they have a higher bias. However, smoothing seems to be useless in the heavy tailed case.

Keywords: Asymptotic Normality; Quantile Function; Tail Index; Monte Carlo Experiment; Free Disposal Hull (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2349-3_1

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DOI: 10.1007/978-3-7908-2349-3_1

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