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Statistica Sinica 17(2007), 1549-1565



V. Roshan Joseph$^1$, Yubin Tian$^2$ and C. F. Jeff Wu$^1$

$^1$Georgia Institute of Technology and $^2$Beijing Institute of Technology

Abstract: The Robbins-Monro procedure (1951) for stochastic root-finding is a nonparametric approach. Wu (1985, 1986) has shown that the convergence of the sequential procedure can be greatly improved if we know the distribution of the response. Wu's approach assumes a parametric model and therefore its convergence rate slows down when the assumed model is different from the true model. This article proposes a new approach that is robust to the model assumptions. The approach gives more importance to observations closer to the root, which improves the fit to the true model around the root and makes the convergence faster. Simulation study shows that the new approach gives a superior performance over the existing methods.

Key words and phrases: Gaussian process, Robbins-Monro procedure, sequential design, stochastic approximation.

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