Asymptotically Distribution-Free Goodness-of-Fit Testing: A Unifying View
提出一个构建渐近分布自由拟合优度检验的通用框架，通过非正交投影将函数类映射到扩展切空间的正交补上，得到变换经验过程，可用于构造多种检验，如Kolmogorov-Smirnov型、Cramer-von Mises型等，且能检测根号n尺度的局部备择假设。
We outline a general paradigm for constructing asymptotically distribution-free (ADF) goodness-of-fit tests, which can be regarded as a generalization of Khmaladze (1993). This is achieved by a nonorthogonal projection of a class of functions onto the ortho-complement of the extended tangent space (ETS) associated with the null hypothesis. In parallel with the work of Bickel et al. (2006), we obtain transformed empirical processes (TEP) which are the building blocks for constructing omnibus tests such as the usual Kolmogorov-Smirnov type tests and Cramer-von Mise type tests, as well as Portmanteau tests and directional tests. The critical values can be tabulated due to the ADF property. All the tests are capable of detecting local (Pitman) alternative at the root-n scale. We shall illustrate the framework in several examples, mostly in regression model specification testing.