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Integrated Square Error Asymptotics for Supersmooth Deconvolution
Author(s) -
HOLZMANN HAJO,
BOYSEN LEIF
Publication year - 2006
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.1467-9469.2006.00517.x
Subject(s) - mathematics , deconvolution , estimator , mean squared error , kernel density estimation , distribution (mathematics) , kernel (algebra) , square (algebra) , blind deconvolution , asymptotic distribution , convergence (economics) , statistics , rate of convergence , density estimation , mathematical analysis , combinatorics , geometry , channel (broadcasting) , engineering , electrical engineering , economics , economic growth
. We derive the asymptotic distribution of the integrated square error of a deconvolution kernel density estimator in supersmooth deconvolution problems. Surprisingly, in contrast to direct density estimation as well as ordinary smooth deconvolution density estimation, the asymptotic distribution is no longer a normal distribution but is given by a normalized chi‐squared distribution with 2 d.f. A simulation study shows that the speed of convergence to the asymptotic law is reasonably fast.