Confidence interval estimation under some restrictions on the parameters with non-linear boundaries

This article deals with the confidence interval estimation of [theta]1, when the parameters [theta]1,[theta]2,...,[theta]k of k populations are subject to some non-linear constraints. We shall consider two types of restrictions (a) [theta] belongs to a k-dimensional ball and (b) k=2 and [theta]1[less-than-or-equals, slant][phi]([theta]2), where [phi](·) satisfies some conditions. In terms of coverage probability of the confidence intervals, it is seen in case of (a) that it does not always pay to use the additional information available on the parameter. This phenomena is also observed when the mean squared error criterion is considered.