Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 1, 138-141

A NOTE ON ASYMPTOTIC NORMALITY FOR DECONVOLUTION KERNEL DENSITY ESTIMATORS

By

YANQIN FAN,

And

YANJUN LIU, University of Windsor, Windsor

SUMMARY. In this note, we derive the asymptotic normality for deconvolution kernel density estimators for ordinary smooth errors that satisfy a weaker condition than that used in Fan (1991 b). Consequently, the result in this paper applies to such typical ordinary smooth errors as gamma, symmetric gamma, and double exponential errors.

AMS (1980) subject classification. 62G05, 60F05

Key words and phrases. Asymptotic normality, deconvolution, nonparametric kernel density estimate, ordinary smooth errors.

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