On the power of some adaptive tests in the one-sample problem (Q5967029)

In some statistical problems the distribution density function is not known. As a result application of adaptive tests in such problems is relatively difficult. In this case one can use estimation of the distribution density function. Power of some adaptive tests with a symmetrical distribution is discussed in this article. A limit of the normalized difference between the power of the best test and the asymptotically efficient adaptive test is found. The limit can be used in investigating the asymptotic deficiency of adaptive tests.