Abstract: Motivated by the goal of improving the efficiency of a sequential design with small sample size, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modeling and nonrecursive iteration. Consistency of the Bayes estimator is established. Simulation studies show its superiority in small-sample performance to Robbins–Monro type procedures. Extension to a version of generalized multivariate quantile is presented.

Bio: Jin Xu is a professor of statistics at East China Normal University. He received his PhD from Bowling Green State University. His research interests include statistical methods in clinical trials, multivariate analysis, and sequential designs.