Nonparametric estimation and testing linear hypotheses in the linear regression model

Abstract

A survey of the latest results in nonparametric hypotheses testing and in nonparametric estimation is given. At first, two main hypotheses usually handled by rank tests, these of randomness and of symmetry, are defined and the locally most powerful rank tests for them described. Aymptotic efficiency considerations are included. In the second part, four rank-estimation procedures for the multiple regression model rue considered. Three of them (those of JUREČKOVÁ, JAECKEL and KOUL) are asymptotically equivalent one to another, the fourth one (KRAFT, VAN EEDEN) combines the classical least-squares estimate with ranks. If the supposed distribution equals to the real one, any of these procedures is asymptotically efficient, as may be seen from the corresponding asymptotic distributions.