Testing for no effect by cosine series methods

The properties of three lack-of-fit tests that are related to non-parametric cosine regression analysis are examined in the context of testing for a constant mean function. Analytic power comparisons of these tests vs a most powerful test are made using intermediate asymptotic relative efficiency. In particular, a data-driven test is produced which is asymptotically as efficient as the most powerful test over a class of alternatives. A small scale simulation experiment Is conducted to ascertain the extent that the large sample comparisons are applicable to finite samples.