Kernel Density Estimation for Heaped Data

Abstract

In self-reported data usually a phenomenon called `heaping' occurs, i.e. survey participants round the values of their income, weight or height to some degree. Additionally, respondents may be more prone to round off or up due to social desirability. By ignoring the heaping process a severe bias in terms of spikes and bumps is introduced when applying kernel density methods naively to the rounded data. A generalized Stochastic Expectation Maximization (SEM) approach accounting for heaping with potentially asymmetric rounding behaviour in univariate kernel density estimation is presented in this work. The introduced methods are applied to survey data of the German Socio-Economic Panel and exhibit very good performance simulations.