Commonality of Cusum, von Neumann and Smoothing-Based Goodness-of-Fit Tests
该文证明Munson-Jernigan和Buckley检验是更广泛非参数检验的特例，并用傅里叶分析比较它们与两个新检验的效力，发现cusum检验对平滑偏离最有效，而基于平滑的检验在高频备择下更优。
Recent papers by Munson & Jernigan (1989) and Buckley (1991) propose nonparametric tests for the hypothesis of no predictor effect in regression. The Munson-Jernigan test is similar to the von Neumann (1941) test, while that of Buckley is based on a functional of cusums. These tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas. Fourier analysis is used to qualitatively compare the Munson & Jernigan and Buckley tests with two new tests constructed from nonparametric smoothers. Their relative powers are then studied by means of large-sample analysis and simulation. The cusum test is the most powerful for very smooth departures from the no-effect hypothesis, while the new tests based on smoothing ideas are clearly superior when the alternative is high frequency.