Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9741803 | Journal of Statistical Planning and Inference | 2005 | 29 Pages |
Abstract
A new strategy is developed for obtaining large-sample efficient estimators of finite-dimensional parameters β within semiparametric statistical models. The key idea is to maximize over β a nonparametric log-likelihood with the infinite-dimensional nuisance parameter λ replaced by a consistent preliminary estimator λËβ of the Kullback-Leibler minimizing value λβ for fixed β. It is shown that the parametric submodel with Kullback-Leibler minimizer substituted for λ is generally a least-favorable model. Results extending those of Severini and Wong (Ann. Statist. 20 (1992) 1768) then establish efficiency of the estimator of β maximizing log-likelihood with λ replaced for fixed β by λËβ. These theoretical results are specialized to censored linear regression and to a class of semiparametric survival analysis regression models including the proportional hazards models with unobserved random effect or `frailty', the latter through results of Slud and Vonta (Scand. J. Statist. 31 (2004) 21) characterizing the restricted Kullback-Leibler information minimizers.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Eric V. Slud, Filia Vonta,