An Introduction to Optimality Criteria and Some Results on Optimal Block Design

X ′Xθ = X ′Y. Here, X ′X is called the “information matrix” of θ and var(θ̂) = σ(X ′X)−1 (provided Rank(X) = t). Let l′θ be an estimable linear parametric function. Then var(l′θ̂) = σ2l′(X ′X)−l. We choose a design d, with design matrix Xd, whose information matrix X ′ dXd is “large” (equivalently, (X ′ dXd) − is “small”) in some sense. Now, suppose we are interested in a component θ1 of θ. We write