Assume $\mathbf{\mu }\sim N\left( 0,I_{r}\right) ,$ where $I_{r}$ is a $% r\times r$ identity matrix, and $\mathbf{y}|\mathbf{\mu }\sim N\left( \mathbf{A\mu },I_{T}\right) ,$ where $\mathbf{A}$ is a $T\times r$ constant matrix and $I_{T}$ is a $T\times T$ identity matrix with $T>r$. My question is how to derive the posterior $\mathbf{\mu }|\mathbf{y}$ such that I can define the James-Stein estimator for $\mathbf{\mu }$. Any suggestions? Thanks
2026-03-26 10:58:29.1774522709
Posterior Distribution and James Stein Estimator
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