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, m_{1}, under a simple order
restriction, m_{1}<=...<=m_{k}.
This article shows that the former estimator of m_{1}
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 m_{1}
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.