Gore, A. P.; Madhava Rao, K. S. Sign and Wilcoxon tests for quadratic versus cubic regression. (English) Zbl 0731.62097 Trab. Estad. Invest. Oper. 35, No. 1, 112-120 (1984). 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 Keywords:nonparametric regression; sign test; Wilcoxon tests; null hypothesis of quadratic regression; cubic regression; Pitman efficiency PDFBibTeX XMLCite \textit{A. P. Gore} and \textit{K. S. Madhava Rao}, Trab. Estad. Invest. Oper. 35, No. 1, 112--120 (1984; Zbl 0731.62097) Full Text: DOI EuDML 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 Unpublished M. Phil.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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.