Further results on the reverse-order law

AbstractAn explicit expression is obtained for a pair of generalized inverses (B−,A−) such that B−A−=(AB)+MN, and a class of pairs (B−,A− of this property is shown. A necessary and sufficient condition for (AB)− to have the expression B−A− is also given

Simultaneous estimation of Poisson means in two-way contingency tables under normalized squared error loss in multiplicative models (Bayesian approaches and statistical inference)

Shrinkage estimation of Poisson means is considered when observations are given in the form of a two-way contingency table. Assuming a multiplicative Poisson model, estimators which shrink to the specified values or an order statistic in one dimension and in two dimensions are considered and are shown to dominate the maximum likelihood estimator (MLE) under normalized squared error loss

Some modifications of improved estimators of a normal variance

Entropy loss, quadratic loss, shrinkage estimator, Stein estimator, uniform risk improvement,

On uniqueness of two principal points for univariate location mixtures

A sufficient condition of uniqueness of two principal points is given for univariate symmetric distributions, which are not necessarily unimodal. Especially a class of location mixtures including the normal ones is shown to have unique two principal points.Bimodal distribution k-means clustering Log-concavity Normal mixture

Precision of individual estimators in simultaneous estimation of parameters

Biases and mean squared errors of estimators of individual parameters are obtained for Stein type estimators of a vector parameter. It is known that for such estimators the average mean squared error over the different parameters under estimation is smaller than that for the usual unbiased estimators. However, such a property may not hold for the mean squared error of any individual estimator for the corresponding parameter. It is found that when a number of parameters are estimated simultaneously by Stein type estimators, some individual estimators have larger mean squared error than those of the usual unbiased estimators and others less. For several combinations of number of parameters and their mean and standard deviation, the range of parameter values for which the Stein type is better has been computed

A Comparison of Restricted and Unrestricted Estimators in Estimating Linear Functions of Ordered Scale Parameters of Two Gamma Distributions

MLE, unbiased estimator, admissible estimator, variance estimation,