On the Loss of Information Due to Nonrandom Truncation

Michael Falk and Frank Marohn

Journal of Multivariate Analysis, 2000, vol. 72, issue 1, 1-21

Abstract: 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.

Keywords: point process; Hellinger distance; statistical experiment; deficiency distance; Blackwell sufficiency; local asymptotic normality; extreme value models; peaks-over-threshold method (search for similar items in EconPapers)
Date: 2000
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