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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.

MSC:

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

[1] Hodges, J. L. Jr., andLehmann, E. L. (1955), The efficiency of some nonparametric competitors of thet-test.Ann. Math. Stats.,27, 324–335. · Zbl 0075.29206 · doi:10.1214/aoms/1177728261
[2] Lehmann, E. L. (1975), Nonparametrics: Statistical Methods Based on Ranks. Holden-day, California. · Zbl 0354.62038
[3] Olshen, R. A. (1967): Sign and Wilcoxon tests for Linearity.Ann. Math. Statist.,38, 1759–1769. · Zbl 0227.62030 · doi:10.1214/aoms/1177698610
[4] Rao, K. S., Madhava (1980), Nonparametric Methods for Regression Analysis. Unpublished M. Phil. Dissertation submitted to University of Poona.
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