| There are many good properties when normal mean is estimated by the corresponding sample mean. But when it is extended to the p-variate normal distribution, what Stein(1956) proved made many statisticians surprised: Let X be a p-variate normal random vector, E (X)=θ,cov( X ,X)=I.When p≥3, X is inadmissible as an estimator ofθ.Under square loss function, the risk of estimator of the form X is less than that of X for a sufficiently small and b sufficiently large. James and Stein (1961) gave the James–Stein estimator X, which dominates X. They also discussed estimator X and indicated that the risk ofδ|^(a)=δJS is minimum when a = p-2.Since the result of Stein(1956), statisticians from all over the world discussed a great number of problems of admissibility. Later, many statisticians put their focuses on James-Stein estimator as well. From then on, James-Stein estimator has been extensively studied, modified, improved, and also applied in many fields. |
