Abstract: This paper first reviews C.Z. Wei's seminal work and subsequent developments in recursive estimation and adaptive control of stochastic regression models and ARMAX systems. By using certain ideas and techniques from these developments, it then develops a new approach to efficient semiparametric estimation in linear time series models.
Key words and phrases: Adaptive control, asymptotic efficiency, least squares, M-estimators, semiparametric estimation, stochastic regression, strong consistency.