Asymptotic Normality of Kernel-Type Deconvolution Estimators |
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Authors: | BERT VAN ES HAE-WON UH |
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Institution: | Korteweg de Vries Institute for Mathematics;and Department of Medical Statistics, Leiden University Medical Center |
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Abstract: | Abstract. We derive asymptotic normality of kernel-type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider so-called super smooth deconvolution problems where the characteristic function of the known distribution decreases exponentially, but faster than that of the Cauchy distribution. It turns out that the limit behaviour of the pointwise estimators of the density and distribution function is relatively straightforward, while the asymptotic behaviour of the estimator of the probability of an interval depends in a complicated way on the sequence of bandwidths. |
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Keywords: | asymptotic normality deconvolution kernel estimation |
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