Shrinkage Estimation of Incomplete Regression Models by Yates Procedure

The problem of estimating the coefficients in a linear regression
model is considered when some of the response values are missing.
The conventional Yates procedure employing least squares
predictions for missing values does not lead to any improvement
over the least squares estimator using complete observations only.
However, if we use Stein-rule predictions, it is demonstrated that
some improvement can be achieved. An unbiased estimator of the mean
squared error matrix of the proposed estimator of coefficient
vector is also presented. Some work on the application of the
proposed estimation procedure to real-world data sets involving
some discrete variables in the set of explanatory variables is
under way and will be reported in future.