Ratio tests under limiting normality
提出一类比率检验，适用于累积数据经适当标准化后渐近正态的情形，利用Karhunen–Loève定理计算加权平均，检验统计量为二次型比率，具有尺度不变性，渐近分布可通过数值方法获得，在避免冗余参数的同时几乎与最优检验同样有效。
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.