The Coupling Spline Model and Stochastic Approximation

Abstract

The seminal work of Robbins and Monro (1951) brought into being a sequential nonparametric procedure to find the root of a regression function. The nonparametric nature of Robbins-Monro scheme allows broad applicability but also causes slower convergence. In this talk, we introduce a new semi-parametric model, the coupling spline model, and construct a coupling algorithm to generate a sequence of approximations to the root. The simulation study demonstrates computational efficiency and faster convergence of the proposed method. With moderate sample sizes, it yields similar accuracy as the optimal Robbins-Monro procedure in the linear case. In other distinctively nonlinear cases, it is 10 to over 1000 times more accurate as measured by mean square error. We then apply the algorithm to compute MLE in some spatial models and generalized linear mixed models.