On confidence sequences for the mean vector of a multivariate normal distribution

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 ...

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...

Screening for a Multivariate Mixture Normal Distribution

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...

Estimation of the mean vector in a singular multivariate normal distribution

This paper addresses the problem of estimating the mean vector of a singular multivariate normal distribution with an unknown singular covariance matrix. The maximum likelihood estimator is shown to be minimax relative to a quadratic loss weighted by the Moore-Penrose inverse of the covariance matrix. An unbiased risk estimator relative to the weighted quadratic loss is provided for a Baranchik...