ON THE ROBUSTNESS OF THE LINEAR-HYPOTHESIS TEST PROCEDURE IN THE SINGULAR LINEAR-MODEL WITH IMPLIED RESTRICTIONS

The linear hypothesis test procedure is considered in the restricted linear models M(r) = {y,X beta parallel to R beta = 0,sigma(2)V} and M(r)* = {y,X beta parallel to AR beta = 0,sigma(2)V}. Necessary and sufficient conditions are derived under which the statistic providing an F-test for the linear hypothesis H-0 : K beta = 0 in the model M(r)*(M(r)) continues to be valid in the model M(r)(M(r)*); the results obtained cover the case where M(r)* is replaced by the general Gauss-Markov model M = {y, X beta, sigma(2)V}.