How Many Iterations Are Sufficient for Semiparametric Estimation?

• Activity Number: 662
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Guang Cheng*+
• Companies: Purdue University
• Keywords: k-step Estimation ; Semiparametric Models ; Higher Order Asymptotic Efficiency ; Newton-Raphson Algorithm ; Initial Estimate

Abstract

In semiparametric models, a common practice in obtaining an efficient estimator for the Euclidean parameter is through iteratively optimizing some objective function w.r.t. its Euclidean parameter and functional parameter via some numerical algorithm. For example, the semiparametric MLE can be obtained by maximizing its profile likelihood via the Newton-Raphson algorithm. The main purpose of this talk is to propose a general approach in constructing such numerical outcome and, more importantly, calculate the minimal number of iterations needed to obtain an efficient estimator from a theoretical point of view. In addition, we also answer the below two questions: (a) what factors determine the higher order asymptotic efficiency of our estimator; (b) how to find a consistent initial estimate for the above iterative procedure.