A class of optimization problems on minimizing variance based criteria in respect of parameter estimators of a linear model

We first consider an optimization problem in which we minimize the average or total variance of the estimators of some parameters of interest in a linear model. In some models, subsets of parameters may be of more interest in this respect than all parameters. We then consider a second optimization problem in which we construct designs achieving equality of variances of the estimators of two linear functions of the parameters. The approaches are formulated for a general regression model, and are explored through some models of interest.