Statistical Tests Based on Transformed Data
研究了原始数据经过变换后在线性模型中检验假设的问题，发现变换参数未知时检验的渐近水平和功效与参数已知时相同，且基于Box-Cox变换的检验在小样本下也有良好表现。
Abstract The problem of testing hypotheses in linear models when the original data have been transformed is considered. It is assumed that the transformation involves an unknown parameter that has to be estimated from the data. For certain important testing problems it is found that the asymptotic level and power is as if λ had been assumed known. Asymptotic efficiency results show that when the Box-Cox transformation is used, tests based on transformed data have good power properties. Simulation results for transformed two-sample and linear regression testing problems show this to be true for moderate to small sample sizes as well. In particular, an α-trimmed t test based on averages of trimmed transformed variables performs very well in both light-tailed and heavy-tailed skew models when compared with the usual t test and rank tests.