A Class of Recursive Algorithms Using Non-parametric Methods with Constant Step Size and Window Width: A Numerical Study
George Yin, Kewen Yin · Contributions to statistics · 1995
Motivated by a wide range of applications in chemical engineering problems, recursive algorithms using nonparametric methods combined with stochastic approximation procedures are developed in this work. Loosely speaking, the problems are to find roots of nonlinear functions provided that only noisy measurements are available. In addition, in the systems under consideration, not only the outputs but also the inputs are noise corrupted. Thus the conventional stochastic approximation algorithms become inapplicable. Algorithms using a kernel function with constant step size and constant window width are proposed and analyzed. After presenting the convergence result of the algorithms under general conditions, effort is directed to the numerical studies. Simulation results and numerical experiments are also given. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.