Nonparametric Density Estimation of a Long-Term Trend from Repeated Semicontinuous Data

Abstract

We consider nonparametric estimation of the density of the long-term trend of a semicontinuous variable observed repeatedly over time. These variables arise when measuring the intensity of an intermittent phenomenon, such as the intake of an episodically consumed nutrient or the concentration of an intermittent toxic substance: when the phenomenon is absent, the measurement is equal to zero; otherwise, it is positive. Semicontinuous data are usually represented by a two-part model describing the zeros and the nonzeros separately, often under parametric assumptions. Recently, Camirand Lemyre, Carroll, and Delaigle showed that it is possible to relax the distributional assumptions on the part ..