In this paper, the estimation of the common mean vector of two multivariate normal populations is considered and a new class of unbiased estimators is proposed. Several dominance results under the quadratic loss and LINEX loss functions are established. To illustrate the usefulness of these estimators, a simulation study with finite samples is conducted to compare them with four existing estimators, including the sample mean and the Graybill-Deal estimator. Based on the comparison studies, we found that the numerical performance of the proposed estimators is almost as good as μ~CC proposed by Chiou and Cohen (Ann Inst Stat Math 37:499–506, 1985) in terms of the risks. Its theoretical dominance over the sample mean of a single population under the sufficient conditions given is also established.
|Title of host publication||Recent Developments in Multivariate and Random Matrix Analysis|
|Subtitle of host publication||Festschrift in Honour of Dietrich von Rosen|
|Editors||Thomas Holgersson, Martin Singull|
|Place of Publication||Netherlands|
|Number of pages||23|
|Publication status||Published - 18 Sep 2020|