Optimized recentered confidence spheres for the multivariate normal mean

Minimum Volume Confidence Regions for a Multivariate Normal Mean Vector

Since Stein’s original proposal in 1962, a series of papers have constructed confidence regions of smaller volume than the standard spheres for the mean vector of a multivariate normal distribution. A general approach to this problem is developed here, and used to calculate a lower bound on the attainable volume. Bayes and fiducial methods are involved in the calculation. Scheffe-type problems ...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Optimal confidence interval for the largest normal mean under heteroscedasticity

A two-stage sampling procedure for obtaining an optimal confidence interval for the largest or smallest mean of k independent normal populations is proposed, where the population variances are unknown and possibly unequal. The optimal confidence interval is obtained by maximizing the coverage probability with a fixed width at a least favorable configuration of means. Then, the sample sizes can ...

Confidence intervals for the normal mean utilizing prior information

Abstract: We consider X1,X2, . . . , Xn that are independent and identically N(μ, σ) distributed random variables. Suppose that the parameter of interest is μ and also suppose that we have uncertain prior information that μ/σ is close to 0. Our aim is to find a frequentist 1 − α confidence interval for μ that utilizes this prior information. Pratt and Brown, Casella and Hwang have described suc...

Multivariate Normal Distribution and Confidence Ellipses

the Normal Distribution's familiar "bell curve". The latter term can be interpreted as a description of squared of distance (x  between some value of x who's probability is being assessed (along the x axis), and  the center of the probability density distribution, "standardized" by the distribution's known variance 2. It should be noted that f(x) only depends on this single scalar range var...