Estimation of Location Parameters from Two Linear Models under Normality

This paper deals with the problem of estimation of common parameters from two linear models under the assumption of normality. A set of sufficient conditions are obtained under which one can uniformly improve upon the estimates obtained from one model. Uniform improvement on both the models is also considered. We construct estimates which satisfy those conditions and apply these methods to (i) the problem of estimating the common mean of two normal populations and (ii) the problem of recovery of interblock information in incomplete block designs. Exact variances for these estimates and for some other estimates have been evaluated for some important special cases and have been computed for some designs.