Model reference adaptive systems applied to regression analyses

The adaptive estimation procedure of model reference adaptive systems is modified and applied to linear models. In general the principle can be used for almost any time series model. Because of the recursive nature of the resulting estimator, it is computationally appealing, especially when a time series is considered as a flow of data. In addition, the estimator turns out to have certain statistical optimality properties. In the linear regression setting, Ridge estimators turn out to constitute a subclass of the adaptive estimators considered, whereas for unknown measurement variance, the resulting estimators are related to James‐Stkintype estimators, and have better properties than the latter. The estimator is shown to be strongly consistent and to converge in law to a normal variate under the standard assumptions of linear models. Further it is shown to be admissible and minimax in restricted parameter spaces. The connection between Kalmanfilters and the classical least‐squares estimator is also pointed out.