Penalized likelihood estimators for truncated data

We investigate the performance of linearly penalized likelihood estimators for estimating distributional parameters in the presence of data truncation. Truncation distorts the likelihood surface to create instabilities and high variance in the estimation of these parameters, and the penalty terms help in many cases to decrease estimation error and increase robustness. Approximate methods are provided for choosing a priori good penalty estimators, which are shown to perform well in a series of simulation experiments. The robustness of the methods is explored heuristically using both simulated and real data drawn from an operational risk context.