Rank procedures for testing subhypotheses in linear regression

Summary In the linear regression modelX _i=α+βc_i+Z_i, we consider the problem of testing the subhypothesis that some (but not all) components of β are equal to 0. A class of asymptotically distribution-free tests based on a quadratic form in aligned rank statistic is studied and the asymptotic relative efficiencies of the proposed tests with respect to the general likelihood ratio test and the test based on least-squares estimates of regression parameters are derived. Asymptotic optimality (à la Wald) is also discussed. Work done under the National Science Foundation Grant MCS 8301409 and NATO Grant 1465.