Maximum Likelihood Estimation of Ratios of Means and Standard Deviations from Normal Populations with Different Sample Numbers under Semi-Order Restriction

Abstract:

      For two normal populations with unknown means $\mu_i $ and variances $\sigma_i^2>0$, $i=1,2$, assume that there is a semi-order restriction between ratios of means and standard deviations and sample numbers of two normal populations are different. A procedure of obtaining the maximum likelihood estimators of $\mu_i$'s and $\sigma_i$'s under the semi-order restrictions is proposed. For $i=3$ case, some connected results and simulations are given.