On Sequential Fixed-Size Confidence Regions for the Mean Vector

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 ...

On Sequential Fixed-width Confidence Intervals for the Mean and Second-order Expansions of the Associated Coverage Probabilities

Confidence Regions for the Mean of a Fuzzy Random Variable

The aim of this paper is to extend the classical problem of confidence interval estimation for the mean of a random variable to the case of a fuzzy random variable. The key idea consists in considering a confidence region defined as a ball w.r.t. a given metric, which is centered in the sample mean and whose radius is determined via bootstrapping. The developed approach is illustrated both by m...

Fixed-width Confidence Interval for a Lognormal Mean

Invariant Empirical Bayes Confidence Interval for Mean Vector of Normal Distribution and its Generalization for Exponential Family

Based on a given Bayesian model of multivariate normal with  known variance matrix we will find an empirical Bayes confidence interval for the mean vector components which have normal distribution. We will find this empirical Bayes confidence interval as a conditional form on ancillary statistic. In both cases (i.e.  conditional and unconditional empirical Bayes confidence interval), the empiri...