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

Bouezmarni, Taoufik; Scaillet, Olivier

doi:10.1017/S0266466605050218

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Title		Consistency of asymmetric kernel density estimators and smoothed histograms with application to income data
Authors		Bouezmarni, Taoufik Scaillet, Olivier
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 kernel — Smoothed histogram — Density estimation — Weak convergence — L_1 consistency — Unbounded density — Boundary bias — Income distribution — Inequality measurement
Identifiers		DOI: 10.1017/S0266466605050218
Full text		Article (Published version) (277 Kb) - Free access
Structures		Faculté d'économie et de management / Geneva Finance Research Institute
Citation (ISO format)		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. doi: 10.1017/S0266466605050218 https://archive-ouverte.unige.ch/unige:35102