Global extrapolation of local efficiency. (English) Zbl 0749.62032
Summary: Given an empirical distribution function test for goodness of fit, it is shown how the second derivative of the asymptotic power function can be employed to obtain global upper bounds for the efficiency. These bounds are least in the class of tests with a convex and centrally symmetric acceptance region. The proof is based on a linear optimization lemma for isotonic critical functions.
MSC:
62G10 | Nonparametric hypothesis testing |
62G30 | Order statistics; empirical distribution functions |