Estimating ordered location and scale parameters

Assume independent random samples are drawn from K populations whose distributions are location, scale, or location-scale families. Let T₁ be an estimator which is admissible for the parameter corresponding to the first population. Next assume that the parameters are ordered. The question addressed is does T₁ remain admissible? For various special cases of the model we exhibit estimators which are better than T₁. The models include estimating a location parameter with squared error loss, estimating a scale parameter with normalized squared error loss, finding a confidence interval for a location parameter, and finding a confidence interval for a normal variance. In these latter models universal domination as defined by Hwang [4] is shown.