Efficiency of estimators for partially specified filtered models
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.
Year of publication: |
1990
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Authors: | Greenwood, P. E. ; Wefelmeyer, W. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 36.1990, 2, p. 353-370
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Publisher: |
Elsevier |
Saved in:
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