Efficiency and deficiency considerations in the symmetry problem

Summary Usually, two statistical procedures A and B are compared by means of their asymptotic relative efficiency e. If e = 1, however, it is more informative to compare A and B by means of the concept of deficiency, which was introduced by H odges and L ehmann 7]. In the present paper we use this concept for the comparison of linear rank tests and parametric tests for the symmetry problem. In this problem, the hypothesis has to be tested that a sample comes from a distribution that is symmetric about zero. The results provide new and strong edivence for the nice performance of linear rank tests for the symmetry problem. The present paper gives a survey of the results obtained by A lbers , B ickel and van Z wet 1] and by A lbers 2].