Eubank, R. L.; Hart, Jeffrey D. Commonality of cusum, von Neumann and smoothing-based goodness-of-fit tests. (English) Zbl 0792.62042 Biometrika 80, No. 1, 89-98 (1993). Summary: Recent papers by P. J. Munson and R. J. Jernigan [ibid. 76, No. 1, 39-47 (1989; Zbl 0664.62068)] and M. J. Buckley [ibid. 78, 253-262 (1991)] propose nonparametric tests for the hypothesis of no predictor effect in regression. The Munson-Jernigan test is similar to the J. von Neumann test [Ann. Math. Statist. 12, 367-395 (1941; Zbl 0060.299)], 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. Cited in 27 Documents MSC: 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics Keywords:Fourier series estimators; local alternatives; nonparametric regression; Pitman relative efficiency; smoothing splines; nonparametric smoothers; relative powers; large-sample analysis; simulation; cusum test Citations:Zbl 0664.62068; Zbl 0060.299 PDFBibTeX XMLCite \textit{R. L. Eubank} and \textit{J. D. Hart}, Biometrika 80, No. 1, 89--98 (1993; Zbl 0792.62042) Full Text: DOI