The present investigation is a follow up of [7] to a class of multiple regression problems, and is devoted to the construction of an estimate of regression parameter vector based on suitable rank statistics. Asymptotic linearity of these rank statistics in the multiple regression set up is established and the asymptotic multi-normality of the derived estimates is deduced. There exists the choice of the score-generating function to every basic distribution so that the asymptotic distribution of the estimates is the same as that of maximal-likelihood estimates.