Linear. empirical bayes estimation in the case of the wishart distribution

We consider independent pairs (X₁,∑₁), (X₂,∑₂),…,(X_n∑_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 X_n+i is obtained, the objective is to estimate ∑ _n+i corresponding to X_n+i. This estimator is called an empirical Bayes (EB) estimator of ∑. We construct a linear EB estimator of ∑ and examine its precision.