Algorithms for Target Estimation using Stochastic Approximation

by Javier Cabrera and Inchi Hu .

Abstract: The target estimation algorithm was first applied in Cabrera, Meer and Leung.(1994), and is designed to reduce bias and median bias. In this paper, we present an algorithm for implementing the target estimation method based on stochastic approximation. The application of stochastic approximation algorithm to target estimation is especially interesting because the bootstrap bias correction procedure corresponds to the first iteration of our algorithm. This rather surprising connection between bootstrap method and target estimation as revealed by stochastic approximation algorithm suggests that when the bias varies considerably as a function of the unknown parameter, one can expect the target estimation to yield substantial improvement over bootstrap bias correction. We also compare the performance of the target estimation method with jackknife and bootstrap through examples from autoregressive models and logistic regression models.

Key Words: Bootstrap, Estimation Equation, Stochastic Approximation

Authors:
Javier Cabrera, cabrera@stat.rutgers.edu
Inchi Hu, imichu@ust.hk

Editor: R.G. Graf, rgraf@sunstroke.sdsu.edu

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