Semiparametric density estimation with localized Bregman divergence

This paper examines semiparametric density estimation by combining a parametric crude guess and its nonparametric adjustment. The nonparametric adjustment is implemented via minimization of the localized Bregman divergence, which yields a broad class of semiparametric density estimators. Asymptotic theories of the density estimators in this general class are developed. Specific concrete forms of density estimators under a certain divergence and parametric guess are calculated. Simulations for several target densities and application to a real data set reveal that the proposed density estimators offer competitive or, in some cases, better performance compared to fully nonparametric kernel density estimator.