Kernel Density Estimation for Heaped Data

Abstract

The phenomenon called “heaping” often occurs in self-reported data, where survey participants round the values of variables such as income, weight, or height to some degree. Respondents may also be more prone to round off or up due to social desirability. By ignoring the heaping process, spurious spikes and bumps are introduced when applying kernel density methods directly to the rounded data. A generalized Stochastic Expectation Maximization (SEM) approach accounting for heaping with potentially asymmetric rounding behavior in univariate kernel density estimation is presented in this work. The proposed methods are applied to survey data of the German Socio-Economic Panel and exhibit very good performance in simulations.