LUO Ping, LI Shuyou, WU Chunjie
In specific practical problems, structures with ordered and inequality constraints find extensive applications in multiple fields. When estimating parameters in such cases, one often encounters restrictions imposed by ordered constraints. For instance, in pharmaceutical testing, researchers may impose constraints on the dosage of a particular drug, necessitating consideration of ordered constraints. Therefore, ordered constraint mean estimation holds significant practical value in these applications. In previous literature, the focus on mean estimation under ordered constraints has been mainly on 2 and 3 multivariate normal populations. This paper extends this focus to the estimation problem of $k$ multivariate normal population means under simple partial order constraints. It introduces a new estimate $\tilde{\mu}$, based on the PAVA algorithm when the population covariance matrix $\Sigma_{i}$ is known, and proves its consistent superiority over the unordered maximum likelihood estimate $\bar{X}$. Finally, the effectiveness of the proposed estimation method is validated through simulation experiments and compared with the maximum likelihood estimation method.
