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Semiparametric Density Deconvolution
Author(s) -
HAZELTON MARTIN L.,
TURLACH BERWIN A.
Publication year - 2010
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.1467-9469.2009.00669.x
Subject(s) - mathematics , estimator , deconvolution , kernel density estimation , semiparametric regression , semiparametric model , parametric statistics , density estimation , kernel (algebra) , parametric model , statistics , combinatorics
. A new semiparametric method for density deconvolution is proposed, based on a model in which only the ratio of the unconvoluted to convoluted densities is specified parametrically. Deconvolution results from reweighting the terms in a standard kernel density estimator, where the weights are defined by the parametric density ratio. We propose that in practice, the density ratio be modelled on the log‐scale as a cubic spline with a fixed number of knots. Parameter estimation is based on maximization of a type of semiparametric likelihood. The resulting asymptotic properties for our deconvolution estimator mirror the convergence rates in standard density estimation without measurement error when attention is restricted to our semiparametric class of densities. Furthermore, numerical studies indicate that for practical sample sizes our weighted kernel estimator can provide better results than the classical non‐parametric kernel estimator for a range of densities outside the specified semiparametric class.