Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 2, pp. 189--201

ON THE IMPROVED ESTIMATION OF LOCATION PARAMETERS SUBJECT TO ORDER RESTRICTIONS IN LOCATION--SCALE FAMILIES

By

STEVEN T. GARREN, James Madison University, Harrisonburg, Virginia

SUMMARY. For some models the isotonic regression estimator is known to universally dominate reasonable unrestricted estimators of the smallest location parameter, m1, under a simple order restriction, m1<=...<=mk. This article shows that the former estimator of m1 fails to dominate the unrestricted maximum likelihood estimator in terms of mean squared error, when the variances are unknown and unequal in a normal model. The former also fails to universally dominate the unrestricted best equivariant estimator, when the scale parameters are known in an exponential model. A different estimator of m1 is shown to universally dominate the unrestricted best equivariant estimator, when the scale parameters are known in an exponential model under more general linear order restrictions. Universal domination results involving the other location parameters and other estimators having lower bounded support also are discussed.

AMS (1991) subject classification. Primary 62F10, 62F30.

Key words and phrases. Exponential distribution, isotonic regression estimator, mean squared error, nodal parameter, normal distribution, order restriction, universal domination.

Full paper (PDF)

This article in Mathematical Reviews