On estimation of parameter functions in a weakly singular linear model with linear inequality restrictions

In this paper, the problem of ICGLS (Inequality Constrained Generalized Least Squares) estimation of a given set function K in the weakly singular model M={y, X| A > b, ^2V} is considered. The ICGLS estimator is not linear and it is expressed in a form of at most of 2^m formulae, where m denotes a number of rows in the matrix A. For a given vector y the one of these formulae can be used. On the basis of the Kuhn-Tucker optimality conditions, necessary and sufficient conditions for a vector Kβ^t to be the ICGLS estimator of Kβ are presented. The estimators are given in explicit form.