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Scientific article
Open access
English

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

Published inEconometric theory, vol. 21, p. 390-412
Publication date2005
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
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
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Article (Published version)
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Identifiers
ISSN of the journal0266-4666
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