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KERNEL ESTIMATION WHEN DENSITY MAY NOT EXIST: A CORRIGENDUM

Published online by Cambridge University Press:  13 September 2016

Victoria Zinde-Walsh
Victoria Zinde-Walsh*
Affiliation:
McGill University and CIREQ
*
*Address correspondence to Victoria Zinde-Walsh, Department of Economics, McGill University, 855 Sherbrooke Street West, Montreal, QC H3A 2T7, Canada; e-mail: victoria.zinde-walsh@mcgill.ca.
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Abstract

The paper “Kernel estimation when density may not exist” (Zinde-Walsh, 2008) considered density as a generalized function given by a functional on a space of smooth functions; this made it possible to establish the limit properties of the kernel estimator without assuming the existence of the density function. This note corrects an error in that paper in the derivation of the variance of the kernel estimator. The corrected result is that in the space of generalized functions the parametric rate of convergence of the kernel density estimator to the limit Gaussian process is achievable.

Type
CORRIGENDUM
Information
Econometric Theory , Volume 33 , Issue 5 , October 2017 , pp. 1259 - 1263
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

The support of the Social Sciences and Humanities Research Council of Canada (SSHRC) and the Fonds québecois de la recherche sur la société et la culture (FRQSC) is gratefully acknowledged. I thank John Galbraith, Yanqin Fan, the Editor and referees for helpful advice.

References

REFERENCES

Brochu, P., Green, D.A., Lemieux, T., & Townsend, J. (2015) The Minimum Wage, Turnover, and the Shape of the Wage Distribution. Working paper, University of British Columbia.Google Scholar
Fortin, N., Lemieux, T., & Firpo, S. (2011) Decomposition methods in economics. In Ashenfelter, O. & Card, D. (eds.), Handbook of Labor Economics, vol. 4A, pp. 1–102. North-Holland.Google Scholar
Gelfand, I.M. & Shilov, G.E. (1964a) Generalized Functions, Volume 1, Properties and Operations. Academic Press.Google Scholar
Gelfand, I.M. & Shilov, G.E. (1964b) Generalized Functions, Volume 2, Spaces of Test Functions and Generalized Functions. Academic Press.Google Scholar
Gelfand, I.M. & Vilenkin, N. Ya. (1964) Generalized Functions, Volume 4, Applications of Harmonic Analysis. Academic Press.Google Scholar
Goldstein, L. & Messer, K. (1992) Optimal plug-in estimators for nonparametric functional estimation. The Annals of Statistics 20, 1306–1328.CrossRefGoogle Scholar
Han, C., Cho, J.S., & Phillips, P.C.B. (2011) Infinite density at the median and the typical shape of stock return distributions. Journal of Business and Economic Statistics 29, 282–294.CrossRefGoogle Scholar
Zinde-Walsh, V. (2008) Kernel estimation when density may not exist. Econometric Theory 24, 696–725.CrossRefGoogle Scholar