Testing linear inequality constraints in the standard linear model

Abstract

In this paper we are concerned with the problem of testing whether the â-parameters of the standard linear model satisfy the linear equality constraints R = r when they are known to satisfy the corresponding linear inequality constraints Râ ⩾ r. In particular we will show that the exact finite sample null distributions of the Likelihood Ratio, Wald and Kuhn-Tucker statistics are known when R is of full row rank but not known when R has less than full row rank. The less than full row rank problem has not been discussed previously but it is of considerable potential importance. This paper contains several simple numerical examples which illustrate the computational details of the tests