Adaptive Designs for Stochastic Root-Finding

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 very different from the true model. This article proposes a new approach that is robust to the model assumptions. The approach utilizes a pinned Gaussian process that 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.