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(Medeen, et all, 1998)" show that Maximum Likelihood estimate is admissible for multinomial distribution under squared error. On other hand, James and Stein showed that arithmetic average is not an admissible estimator of Gaussian location parameter in 3 dimensions. But since maximum likelihood estimates of multinomial parameters are averages of observed counts, which become normally distributed for large sample sizes, why doesn't Stein effect happen here?

$\hat{p}$ is an inadmissible estimator of $\theta$ if there's an estimator that is no worse for every $\theta$ and better for at least one

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# Why doesn't Stein effect happen for multinomial distributions?

(Medeen, et all, 1998)" show that Maximum Likelihood estimate is admissible for multinomial distribution under squared error. On other hand, James Stein showed that arithmetic average is not an admissible estimator of Gaussian location parameter in 3 dimensions. But since maximum likelihood estimates of multinomial parameters are averages of observed counts, which become normally distributed for large sample sizes, why doesn't Stein effect happen here?

$\hat{p}$ is an inadmissible estimator of $\theta$ if there's an estimator that is no worse for every $\theta$ and better for at least one