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Information bounds for nonparametric estimators of L-functionals and survival functionals under censored data

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  • Arnold Janssen

  • Andreas Knoch

Abstract

In the present paper we derive lower asymptotic information bounds of Cramér-Rao type for estimators of nonparametric statistical functionals. The results are based on dense differentiability and dense regularity concepts which lead to weak assumptions. As explicit examples L-estimators are treated. In addition a new rapid method for the treatment of survival functionals under randomly right censored data is presented. For instance, for the famous Kaplan-Meier and Nelson-Aalen estimators, our information bound is just the lower bound obtained earlier in the literature. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Arnold Janssen & Andreas Knoch, 2016. "Information bounds for nonparametric estimators of L-functionals and survival functionals under censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 195-220, February.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:2:p:195-220
    DOI: 10.1007/s00184-015-0551-y
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    References listed on IDEAS

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    1. Arnold Janssen & Stefan Wellek, 2010. "Exact linear rank tests for two‐sample equivalence problems with continuous data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(4), pages 482-504, November.
    2. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2452-2463, November.
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    5. A. Janssen, 1989. "Local asymptotic normality for randomly censored models with applications to rank tests," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 43(2), pages 109-125, June.
    6. Einmahl, J.H.J., 1996. "A short and elementary proof of the main Bahadur-Kiefer theorem," Other publications TiSEM bd980f38-c118-4174-9816-8, Tilburg University, School of Economics and Management.
    7. Janssen, Arnold, 1994. "On local odds and hazard rate models in survival analysis," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 355-365, August.
    8. Janssen, Arnold, 2003. "A nonparametric Cramer-Rao inequality for estimators of statistical functionals," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 347-358, October.
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