Maximum Likelihood Recursion and Stochastic Approximation in Sequential Designs

摘要

When the saving of sample size is an important consideration, sequential design of experiments is often used. By efficiently utilizing the information in the past experiments, it determines how the next experiment should be conducted. Statistical theory for sequential designs has been developed for normal and binomial variations. For the problem of determining the solution of an unknown nonlinear equation, we have developed a class of sequential design procedures that can handle very general variations described by the generalized linear models. In special cases it includes a new adaptive version of the Robbins-Monro stochastic approximation and a maximum likelihood recursion scheme for quantal responses. Its relation to the stochastic approximation and the role the link function plays are studied. Theoretical issues such as consistency, robustness, asymptotic normality and second-order properties are discussed.