回帰分析における誤差分散のスタイン型改良信頼区間の諸性質

In this paper the interval estimation of the disturbance variance in a linear regression model is discussed from several view points. Firstly, a brief summary ofthe Stein type point estimation theory and the Stein type interval estimation theory is given. Then, the relationship between the improvement on the point estimation and the improvement on the interval estimation is discussed. It is shown that substituting the Stein type estimator for the usual estimator in the confidence interval leads to the improvement on the interval estimation. Secondly, the Neyman accuracy of the Stein type confidence interval is considered. The Neyman accuracy is a measure related to the unbiasedness of a confidence interval. It is shown that the Stein type confidence interval is not unbiased. Thirdly, the Wolfowitz accuracy of the Stein type confidence interval is considered. The Wolfowitz accuracy is related to the closeness of the endpoints to. the true parameter. The sufficient condition for the Stein type confidence interval to improve on the usual confidence interval is derived. Finally, the Stein type confidence interval is discussed under the multivariate Student-t distribution. It is shown that so far as the coverage probability and the multivariate Student-t distributions are concerned, the Stein type confidence interval is not robust against nonnormality, but that the superiority over the usual confidence interval still holds against nonnormality. Furthermore, for the case when it is known that error terms have a multivariate Student-t distribution, a Stein type confidence interval which improves on the usual confidence interval is presented.

論説 (Article)