An M-Theorem for Semiparametric Models with Bundled Parameters

• Activity Number: 55
• Type: Invited
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Ying Ding and Bin Nan*+
• Companies: Eli Lilly and Company and University of Michigan
• Keywords: Accelerated failure time model ; B-spline ; bundled parameters ; efficient score function ; semiparametric efficiency ; sieve maximum likelihood estimation

Abstract

In many semiparametric models that are parameterized by two types of parameters -- an Euclidean parameter of interest and an infinite dimensional nuisance parameter, the two parameters are bundled together, i.e., the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument. For example, in a linear regression model for censored survival data, the unspecified error distribution function involves the regression coefficients. Motivated by developing an efficient estimating method for the regression parameters, we propose a general M-theorem for bundled parameters and apply the theorem to deriving the asymptotic theory for the sieve maximum likelihood estimation in the linear regression model for censored survival data. The numerical implementation of the proposed estimating method can be achieved through the conventional gradient-based search algorithms such as the Newton-Raphson algorithm. We show that the proposed estimator is consistent, asymptotically normal and achieves the semiparametric efficiency bound. Finite sample performance is evaluated by simulations.