Confidence Set based on James-Stein Estimator

What is it about?

We establish how the asymptotic expansions for the coverage probability of confidence set centered at the James-Stein can be used for a construction of confidence region with constant confidence level, which is asymptotically equal to some fixed value $1-\alpha$.

Featured Image

Why is it important?

A confidence region $D$ with confidence level, which is asymptotically ($\tau\to 0$ or $\tau \to \infty$) equal to fixed value, may be much smaller by size than used confidence set $D_{\delta^+}$. A point $\tau$ is detected, starting from which a quick decreasing of coverage probability of true parametric values by the region $D$ appears. This provides us an interval of values of $\tau$ when it is preferable to use of the confidence region $D$, than the usual confidence set $D_{\delta^+}$.