Asymptotic normality of kernel type deconvolution estimators

Details Asymptotic normality of kernel type deconvolution estimators Asymptotic normality of kernel type deconvolution estimators

2001-12-04

arxiv.org/abs/math/0112032v1

Mathematics

Statistics Theory

26 pages

Scientific paper

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 the so called super smooth case where the characteristic function of the known distribution decreases exponentially. It turns out that the limit behavior of the pointwise estimators of the density and distribution function is relatively straightforward while the asymptotics of the estimator of the probability of an interval depends in a complicated way on the sequence of bandwidths.

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