Sign and Wilcoxon tests for quadratic versus cubic regression. (English) Zbl 0731.62097

Summary: Sign and Wilcoxon tests for testing the null hypothesis of quadratic regression versus the alternative, cubic regression, are proposed. It is shown that in the case of a simple design consisting of multiple Y observations at each of the four levels of x the proposed tests perform reasonably well as compared to their parametric competitors, while in the case of a general design consisting of a large number of levels of x, the loss in Pitman efficiency is considerable. However their computational simplicity appears remarkable.


62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62K99 Design of statistical experiments
62J05 Linear regression; mixed models
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