Tweedie-based nonparametric estimation for semicontinuous mixed densities

TL;DR

This paper introduces a Tweedie-based asymmetric kernel estimator for semicontinuous data, effectively handling boundary effects and mixed distributions, with proven theoretical properties and practical advantages demonstrated through simulations and real data.

Contribution

It develops a novel nonparametric estimator tailored for semicontinuous outcomes using Tweedie kernels, including theoretical analysis and a data-driven bandwidth selection method.

Findings

Estimator performs well in boundary-spike and heavy-tailed scenarios.

Theoretical results include bias, variance, and asymptotic normality.

Application to healthcare data demonstrates practical utility.

Abstract

Semicontinuous outcomes occur frequently in health services, insurance, and cost studies. Standard nonparametric density estimators are not well suited to such data because they do not naturally accommodate the mixed structure, the nonnegative support, or the pronounced boundary effects near zero. To address these limitations, we introduce an asymmetric kernel estimator for mixed densities on $[0,\infty)$ based on the Tweedie distribution. For a power parameter $p\in(1,2)$, the Tweedie kernel itself has a point mass at zero and an absolutely continuous component on $(0,\infty)$, yielding a unified smoothing construction that preserves the atom at zero and smooths the positive component using the full semicontinuous sample. We establish pointwise bias and variance expansions, derive asymptotic formulae for the mean squared error and mean integrated squared error, obtain optimal bandwidth rates, and prove asymptotic normality. We propose a profile least-squares cross-validation procedure to jointly select the bandwidth and the power parameter. Simulation results show competitive performance, particularly in challenging boundary-spike and heavy-tailed settings, and an application to emergency department length-of-stay data illustrates the practical value of the method.