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This study establishes the asymptotic consistency of the James-Stein shrinkage estimator (JSSE) ˆ!⇤ n of some parameter ✓, which is obtained by shrinking a maximum likelihood estimator (MLE) ˆ✓n. Our shrinking strategy involves creating a subspace to shrink to by partitioning the parameter space...

In this dissertation, we examine the small and large sample properties of the U-statistics (Un) for an estimable parameter : For small sample, Un is found to be MVUE and Su cient. Large sample properties of Un examined are Consistency and Asymptotic normality. We also compare the rate of...