Order restricted estimators: some bias results

Abstract

Stimulated by practical concerns in the use of order restricted estimators, we study some bias issues of isotonic estimators of ordered parameters. We obtain explicit expressions for biases of order restricted estimators of ordered means of two normal populations with common variance. Based on intuitive considerations, we also propose a new estimator of the common variance of two normal populations having ordered normal means and show that it has smaller bias than the maximum likelihood estimator of the variance and has smaller mean squared error than the usual unbiased estimator of the common variance.