COMMONALITY OF CUSUM, VONNEUMANN AND SMOOTHING-BASED GOODNESS-OF-FIT TESTS

Recent papers by Munson & Jernigan (1989) and Buckley (1991) propose n onparametric tests for the hypothesis of no predictor effect in regres sion. The Munson-Jernigan test is similar to the von Neumann (1941) te st, while that of Buckley is based on a functional of cusums. These te sts are shown to be special cases of a wider class of tests based on n onparametric function estimation ideas. Fourier analysis is used to qu alitatively compare the Munson & Jernigan and Buckley tests with two n ew tests constructed from nonparametric smoothers. Their relative powe rs are then studied by means of large-sample analysis and simulation. The cusum test is the most powerful for very smooth departures from th e no-effect hypothesis, while the new tests based on smoothing ideas a re clearly superior when the alternative is high frequency.