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Asymptotic Normality of Kernel‐Type Deconvolution Estimators
Author(s) -
ES BERT VAN,
UH HAEWON
Publication year - 2005
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2005.00443.x
Subject(s) - mathematics , deconvolution , pointwise , estimator , asymptotic distribution , cauchy distribution , probability density function , kernel (algebra) , kernel density estimation , statistics , mathematical analysis , combinatorics
. 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.