ABSTRACT
Inspection of Table 2 reveals that rank tests can be substantially more powerful (in the local, Pitman sense) than their classical Gaussian counterparts. The asymptotic relative efficiency of rank tests of the Laplace type with respect to classical procedures is as high as 2, which means that they consume about 50 per cent less observations to achieve the same asymptotic result! The van der Waerden tests yield AREs strictly larger than one under logistic and double exponential densities. It can be shown, Hallin ( 1994), that this is a general result, extending to the time-series context the traditional Chernoff-Savage ( 19 58) property of normal scores:
( 5.26)
where the inf.~ is attained at Gaussian g only. The very strong implication of this generalized Chernoff-Savage result is that van der Waerden tests are always strictly more powerful, in the Pitman sense, than the traditional ones-except, of course, under Gaussian densities, where both are asymptotically equivalent.
