Deconvolution with Unknown Error Distribution

Abstract

We consider the errors-in-variables problem of estimating the distribution of a variable X observed with classical measurement errors. In the nonparametric literature, it is often assumed that the error density is perfectly known but in applications this is often too restrictive. We present approaches for non- and semiparametric inference procedures that do not assume the error density to be fully known, and consider the heteroscedastic errors variant of this deconvolution problem. There are two ways to avoid assuming that the error density is known: either we observe additional data (repeated contaminated measurements, longitudinal data, validation data, auxiliary variables, instrumental va..