Linear empirical Bayes estimation in the case of the Wishart distribution
empirical Bayes estimation; the Wishart distribution; COVARIANCE-MATRIX; MINIMAX ESTIMATORS; MOMENTS; Statistics & Probability
We consider independent pairs (X-1, Sigma(1)), (X-2, Sigma(2)), ..., (X-n, Sigma(n)), where each Sigma(i) is distributed according to some unknown density function g(Sigma) and, given Sigma(i) = Sigma, X-i has a conditional density function q(x\Sigma) of the Wishart type. In each pair, the first component is observable but the second is not. After the (n + 1)-th observation Xn+1 is obtained, the objective is to estimate Sigma(n+1) corresponding to Xn+1. This estimator is called an empirical Bayes (EB) estimator of Sigma. We construct a linear EB estimator of Sigma and examine its precision.
Communications in Statistics-Theory and Methods
Pensky, M., Kirtane, K. (2000). Linear empirical Bayes estimation in the case of the Wishart distribution. Communications in Statistics-Theory and Methods, 29(8). doi: 10.1080/03610920008832578