A Skewed Version of the Robbins-Monro-Joseph Procedure for Binary Response

• Activity Number: 470
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Defense and National Security
• Author(s): Dianpeng Wang*+ and Yubin Tian and C. F. Jeff Wu
• Companies: Beijing Institute of Technology and Beijing Institute of Technology and Georgia Institute of Technology
• Keywords: Robbins-Monro stochastic approximation ; Asymmetric loss function ; Extreme quantiles

Abstract

The Robbins-Monro stochastic approximation has been used in sensitivity testing experiments. Joseph (2004) recognized that the procedure is not well suited for binary data and proposed a modification which gives better performance for p between 0.1 and 0.9. However, for extreme p values, say p>0.01 or p< 0.99, which is used for high precision requirement, this modification does not perform well. Here we propose a skewed version of the Robbins-Monro-Joseph procedure based on an asymmetric loss function. It can speed up convergence by employing different penalties for under-shooting and over-shooting to reduce the expected loss. Simulation studies show that this new procedure performs substantially better for extreme quantiles.