Testing the Linearity Hypothesis Using Power Transformations
Yaein Baek, Jin Seo Cho · 2013
We consider a method to test the linearity hypothesis using power transformations. The linear model hypothesis can be derived from a power transformation in three different ways, and each way yields an identification problem. We call this the threefold identification problem and show that the quasi-likelihood ratio (QLR) statistic can overcome the identification problem. Specifically, we approximate the QLR statistic under each identification problem and show that the separately obtained null approximations can be combined so that the null approximation is obtained under the linear model hypothesis. We further consider generalizing the Box-Cox transformation, which we associate with the QLR test statistic.