Weighted Likelihood for Semiparametric Models and Two-phase Stratified Samples, with Application to Cox Regression
We consider semiparametric models for which solution of Horvitz-Thompson or inverse probability weighted (IPW) likelihood equations with two-phase stratified samples leads to <formula format="inline"><file name="sjos_523_mu1.gif" type="gif" /></formula> consistent and asymptotically Gaussian estimators of both Euclidean and non-parametric parameters. For Bernoulli (independent and identically distributed) sampling, standard theory shows that the Euclidean parameter estimator is asymptotically linear in the IPW influence function. By proving weak convergence of the IPW empirical process, and borrowing results on weighted bootstrap empirical processes, we derive a parallel asymptotic expansion for finite population stratified sampling. Several of our key results have been derived already for Cox regression with stratified case-cohort and more general survey designs. This paper is intended to help interpret this previous work and to pave the way towards a general Horvitz-Thompson approach to semiparametric inference with data from complex probability samples. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..
Year of publication: |
2007
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Authors: | BRESLOW, NORMAN E. ; WELLNER, JON A. |
Published in: |
Scandinavian Journal of Statistics. - Danish Society for Theoretical Statistics, ISSN 0303-6898. - Vol. 34.2007, 1, p. 86-102
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Publisher: |
Danish Society for Theoretical Statistics Finnish Statistical Society Norwegian Statistical Association Swedish Statistical Association |
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