Reducing variance and improving bandwidth selection in density estimation via semiparametric transformations and local linear smoothing

Abstract This paper introduces a novel density estimator that combines an initial parametric approximation with a boundary-aware correction factor based on a semiparametric data transformation. The main contributions include achieving bias reduction comparable to existing semiparametric methods while simultaneously reducing estimation variance more effectively than current techniques, and developing a MISE-optimal plug-in bandwidth selector based on the initial parametric density estimator. The asymptotic distribution of the proposed data–driven bandwidth and its faster convergence to the ‘ideal’ bandwidth, compared to standard nonparametric methods, are established analytically herein. The improvement in finite sample estimation performance is demonstrated analytically as well as through both simulations and real data analysis, particularly in scenarios involving complex density features, such as multiple modes.