(1) Department of Mathematics, Graduate School, University of Science and Technology of China, 100039 Beijing, China;(2) Institute of Applied Mathematics, Chinese Academy of Sciences, 100080 Beijing, China
Abstract:
An example is given to reveal the abnormal behavior of the least squares estimate of multiple regression. It is shown that
the least squares estimate of the multiple linear regression may be “improved” in the sense of weak consistency when nuisance
parameters are introduced into the model. A discussion on the implications of this finding is given.