On the Loss of Information Due to Nonrandom Truncation

It is assumed that observations among an iid sample falling into certain subsets of the sample space cannot be observed directly, but only through their frequencies. Bounds for the corresponding loss of information are established, which are based on the Hellinger distance between the empirical point process Nn of the complete set of observations and an empirical process N*n that aims at restoring Nn. An application of these bounds to parametric models generalizes and quantifies results for locally asymptotically Gaussian experiments. When applied to extreme value models, this approach generalizes the peaks-over-threshold method for modeling the exceedances over high thresholds in an iid sample.