Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom