Shrinkage-based semiparametric density estimation

Abstract

Shrinkage estimation is used to develop a semiparametric density estimator as a linear combination of a fully known parametric density function and a nonparametric density estimator. We determine the asymptotic properties of the shrinkage coefficient and of the semiparametric estimator’s integrated squared error. Moreover, we show that the proposed estimation methodology delivers density estimators that are more accurate than nonparametric estimators and that do not require the use of optimal smoothing parameters.