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Efficiency of estimators for partially specified filtered models

Author

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  • Greenwood, P. E.
  • Wefelmeyer, W.

Abstract

Let Xn1,..., Xnn be counting processes and let Yn1,..., Ynn be vector-valued covariate processes. Assume that the intensity processes of the Xni with respect to the filtration generated by Xni and Yni are known up to a (possibly infinite-dimensional) parameter, but that the distribution of Xni and Yni is unspecified otherwise. We give conditions under which the partially specified likelihood in the sense of Gill-Slud-Jacod is locally asymptotically normal. We show that the partially specified likelihood determines a covariance bound in the sense of a Hájek-LeCam convolution theorem for estimating functionals of the underlying parameter. The theorem shows that the Huffer-McKeague estimator is efficient in Aalen's additive risk model, and that the Cox estimator for the regression coefficients and a Breslow-type estimator for the integrated baseline hazard are efficient in Cox's and in Prentice and Self's proportional hazards models.

Suggested Citation

  • Greenwood, P. E. & Wefelmeyer, W., 1990. "Efficiency of estimators for partially specified filtered models," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 353-370, December.
  • Handle: RePEc:eee:spapps:v:36:y:1990:i:2:p:353-370
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    Cited by:

    1. Zhang, Haimeng & Goldstein, Larry, 2003. "Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 292-317, May.
    2. P. B. Seetharaman, 2004. "The Additive Risk Model for Purchase Timing," Marketing Science, INFORMS, vol. 23(2), pages 234-242, March.

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