Maximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances

To analyze the isotonic regression problem for normal means, it is usual to assume that all variances are known or unknown but equal. This paper then studies this problem in the case that there are no conditions imposed on the variances. Suppose that we have data drawn fromkindependent normal populations with unknown meansμiʹs and unknown variancesσ2iʹs, in which the means are restricted by a given partial ordering. This paper discusses some properties of the maximum likelihood estimates ofμiʹs andσ2iʹs under the restriction and proposes an algorithm for obtaining the estimates.