Linear. empirical bayes estimation in the case of the wishart distribution
We consider independent pairs (X1,∑1), (X2,∑2),…,(Xn∑n), where each Si is distributed according to some unknown density function g(∑) and, given ∑i = ∑, X has a conditional density function g(x|∑) of the Wishart type. In each pair, the first component is observable but the second is not. After the (n + l)-th observation Xn+i is obtained, the objective is to estimate ∑ n+i corresponding to Xn+i. This estimator is called an empirical Bayes (EB) estimator of ∑. We construct a linear EB estimator of ∑ and examine its precision.