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Title

Consistency of asymmetric kernel density estimators and smoothed histograms with application to income data

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Bouezmarni, Taoufik
Published in Econometric Theory. 2005, vol. 21, p. 390-412
Abstract We consider asymmetric kernel density estimators and smoothed histograms when the unknown probability density function f is defined on [0,+infinity). Uniform weak consistency on each compact set in [0,+infinity) is proved for these estimators when f is continuous on its support. Weak convergence in L_1 is also established. We further prove that the asymmetric kernel density estimator and the smoothed histogram converge in probability to infinity at x=0 when the density is unbounded at x=0. Monte Carlo results and an empirical study of the shape of a highly skewed income distribution based on a large micro-data set are finally provided.
Keywords Asymmetric kernelSmoothed histogramDensity estimationWeak convergenceL_1 consistencyUnbounded densityBoundary biasIncome distributionInequality measurement
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BOUEZMARNI, Taoufik, SCAILLET, Olivier. Consistency of asymmetric kernel density estimators and smoothed histograms with application to income data. In: Econometric Theory, 2005, vol. 21, p. 390-412. https://archive-ouverte.unige.ch/unige:35102

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Deposited on : 2014-03-31

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