General Departmental Seminar Series
The Piggyback Bootstrap for Functional Inference in Semiparametric Models
John Dixon, Ph.D. candidate, Department of Statistics, UW-Madison
Friday, Jan 24, 2003, 4:00-5:00
Room 6225, Medical Sciences Center, 1300 University Ave.
We consider bootstrap confidence sets for a general class of semiparametric models that includes frailty regression models arising in survival analysis and biased sampling models that have application to vaccine efficacy trials. We propose a computationally efficient Monte Carlo method for accurately approximating the joint limiting distribution of the maximum likelihood estimators for both the parametric and nonparametric components. The main theoretical contribution is that the orthogonality between the efficient score for the parametric component and the usual score for the nuisance parameter can be utilized to dramatically reduce the dimension of the required maximization problem in comparison to the standard bootstrap. This is accomplished by first obtaining a valid Monte Carlo draw for the parametric component, and then obtaining a "piggybacked" bootstrap draw for the nonparametric component. The piggyback step is achieved by maximizing a bootstrapped likelihood with the parametric component fixed at the value of the parametric draw. Bootstrap confidence sets from the piggyback and ordinary bootstraps are compared for survival data arising in a non-Hodgkin's lymphoma study and for biased sampling data from simulated vaccine efficacy trials.
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