A Comparison of james–sten regression with least squares in the pitman nearness sense

Abstract

The least squares ectimatnr and the James-Stein estimator of rhe vector-valued parameter in a multiple linear regression model are compared in thc Pitman searness sense. A table of the comparison is presented, and the James—Siein esiiriiaior is fad to be uniform!y preferred te the least squares in this sense. In many practical situations the James-Stein estimate is extremely close to the least squares estimate, and so is barely preferred in the Pitman nearness sense. However, there are practical situations in which the James—Stein estimate is sufficiently different from the least squares estimate to be substantially better in the Pitman nearness sense.

Keywords:

• Multiple regression
• Rao's noncentral F.