Linear regression with randomly double-truncated data

Abstract

Non-parametric estimation for a linear regression model under random double-truncation is investigated, i.e. the variables are observed if and only if the dependent variable lies in a random interval. The method requires only weak distribution assumptions to ensure identifiability, but does not require any specific distribution family for any variable, neither for the truncation variables nor for the error term. By using non-parametric estimators of several distribution functions, consistent and asymptotically normal estimators are established. A simulation study shows the tendency that the lower the probability of observation, the higher the mean squared error of the estimators, even for the same number of observations. Finally, the method is applied to a doubly truncated data set of German companies, where the age-at-insolvency is of interest.