1986 年 13 巻 20 号 p. 13-21
We consider the polynomial regression model. In this model a hierarchical structure, or natural ordering, in the parameter space can be assumed.
Maximum likelihood estimators may be found for the parameters of each order model in the hierarchy. We introduce the class of estimators given by weighted combinations of these maximum likelihood estimators under certain restrictions. This class is obtained by considering a Bayes estimator class and contains the subset regression estimator as a special case.
The optimal weights which minimize the predictive mean squared error are obtained exactly, using an alternative method to that of Kanda (1985). The estimated weights which minimize the estimated predictive mean square error in a similar way to the Mallow's Cp-statistic are also exactly presented and some numerical examples are shown.
