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On the Loss of Information Due to Nonrandom Truncation

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  • Falk, Michael
  • Marohn, Frank

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.

Suggested Citation

  • Falk, Michael & Marohn, Frank, 2000. "On the Loss of Information Due to Nonrandom Truncation," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 1-21, January.
    • Handle: RePEc:eee:jmvana:v:72:y:2000:i:1:p:1-21
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    References listed on IDEAS

    as
    1. Marohn F., 1995. "Neglecting Observations In Gaussian Sequences Of Statistical Experiments," Statistics & Risk Modeling, De Gruyter, vol. 13(1), pages 83-92, January.
    2. Michael Falk, 1995. "LAN of extreme order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 693-717, December.
    3. Borm, Peter & Keiding, H & McLean, R.P. & Oortwijn, S & Tijs, S, 1992. "The Compromise Value for NTU-Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 175-189.
    4. Marohn F., 1999. "Local Asymptotic Normality Of Truncation Models," Statistics & Risk Modeling, De Gruyter, vol. 17(3), pages 237-254, March.
    5. Janssen, A. & Marohn, F., 1994. "On statistical information of extreme order statistics, local extreme value alternatives, and poisson point processes," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 1-30, January.
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