# Shrinkage estimation of Efron and Morris (1972)

I read this article: Article1 and which was refined by the second article Article2 that was considered as a generalization of the James-Stein estimator.

In article 1 for example, they considered the following estimator:

$\sum' = [a S^{-1} + (b/trace(S))I]^{-1}$

where $a = k-p-1$ and $b = p(p+1) -2$ and $k>p+1$.

After I read the two articles, I became a little bit confused.

(1) Do they always consider that the true covariance matrix $\sum$ is proportional to the identity matrix (i.e., $\sum= \gamma I$), where $\gamma$ is a constant? And finally they give us the new shrinkage estimator based only on this assumption?

(2) If the answer of question (1) is yes, their proposed shrinkage estimator will not become accurate if we assume that the true covariance matrix $\sum$ is not proportional to the identity matrix. Am I wrong?