Nonparametric regression estimation from data contaminated by a mixture of Berkson and classical errors

Estimation of a regression function is a well known problem in the context of errors in variables, where the explanatory variable is observed with random noise. This noise can be of two types, known as classical or Berkson, and it is common to assume that the error is purely of one of these two types. In practice, however, there are many situations where the explanatory variable is contaminated by a misture of the two errors. In such instances, the Berkson component typically arises because the variable of interest is not directly available and can only be assessed through a proxy, whereas the innaccuracy related to the observation of the latter causes an error of classical type. In this paper we propose a nonparametric extimator of a regression function from data contaminated by a mixture of the two errors. We prove consistency of our estimator, derive rates of convergence and suggest a data-driven implementation. Finite-sample performance is illustrated via simulated and real-data examples.