TY - DATA T1 - Ratio tests under limiting normality PY - 2018/01/22 AU - Uwe Hassler AU - Mehdi Hosseinkouchack UR - https://tandf.figshare.com/articles/journal_contribution/Ratio_tests_under_limiting_normality/5809677 DO - 10.6084/m9.figshare.5809677.v1 L4 - https://ndownloader.figshare.com/files/10270704 KW - Asymptotic power KW - likelihood ratio KW - local alternatives KW - self-normalization KW - variance ratio KW - C12 KW - C20 N2 - We propose a class of ratio tests that is applicable whenever a cumulation (of transformed) data is asymptotically normal upon appropriate normalization. The Karhunen–Loève theorem is employed to compute weighted averages. The test statistics are ratios of quadratic forms of these averages and hence scale-invariant, also called self-normalizing: The scaling parameter cancels asymptotically. Limiting distributions are obtained. Critical values and asymptotic local power functions can be calculated by standard numerical means. The ratio tests are directed against local alternatives and turn out to be almost as powerful as optimal competitors, without being plagued by nuisance parameters at the same time. Also in finite samples they perform well relative to self-normalizing competitors. ER -