| Abstract: | Recent articles 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. Fourier analysis is used to show that these tests are special cases of a wider class of tests based on nonparametric smoothing ideas. The relative power of the tests is 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 tests based on smoothing ideas are clearly superior when the alternative is high frequency. Since the smoothing-based tests also have reasonable power when the alternative is smooth, they appear to be a good choice when the type of alternative cannot be anticipated. |
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