Density estimation for data with rounding errors

Rounding of data is common in practice. The problem of estimating the underlying density function based on data with rounding errors is addressed. A parametric maximum likelihood estimator and a nonparametric bootstrap kernel density estimator are proposed. Simulations indicate that the maximum likelihood approach performs well when prior information on the functional form of the underlying distribution is available, while the kernel-type estimator attains stable and good performance in various cases. The proposed methods are further applied to detect the distributional difference of head circumferences from two Chernobyl impacted regions of Ukraine.