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Testing a linear regression model against nonparametric alternatives. (English) Zbl 0785.62049
Summary: As a test statistic for testing goodness-of-fit of a linear regression model, we propose a ratio of quadratic forms measuring the distance between parametric and nonparametric fits, relative to the estimated error variance. The test statistic is a modification of the statistic suggested by W. Härdle and E. Mammen [Comparing nonparametric versus parametric regression fits. Preprint (1988)]. The asymptotic distribution under the hypothesis is established. The finite sample behaviour of the test is investigated in a Monte Carlo study, and is illustrated for two applications.

MSC:
62G10 Nonparametric hypothesis testing
62J05 Linear regression; mixed models
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[1] Atkinson AC (1985) Plots, Transformations, and Regression. Clarendon Press, Oxford · Zbl 0582.62065
[2] de Jong P (1987) A Central Limit Theorem for Generalized Quadratic Forms.Probability Theory and Related Fields 75:261–277 · Zbl 0596.60022 · doi:10.1007/BF00354037
[3] Elston DA, Glasbey CA, Neilson DR (1989) Non-Parametric Lactation Curves.Animal Production 48:331–339 · doi:10.1017/S0003356100040320
[4] Eubank RL, Spiegelman CH (1990) Testing the Goodness of Fit of a Linear Model Via Nonparametric Regression Techniques.Journal of the American Statistical Association 85:387–392 · Zbl 0702.62037 · doi:10.2307/2289774
[5] Gasser Th, Müller HG (1979) Kernel Estimation of Regression Functions.
[6] Gasser Th, Rosenblatt M (Ed) Smoothing Techniques for Curve Estimation, 23–68,Lecture Notes in Mathematics 757, Springer-Verlag, Berlin
[7] Gasser Th, Sroka L, Jennen-Steinmetz C (1986) Residual Variance and Residual Pattern in Nonlinear Regression.Biometrika 73:625–633 · Zbl 0649.62035 · doi:10.1093/biomet/73.3.625
[8] Härdle W, Mammen E (1988) Comparing Nonparametric versus Parametric Regression Fits. Preprint · Zbl 0795.62036
[9] Härdle W (1990) Applied Nonparametric Regression. Cambridge University Press, Cambridge; Section 9.3, pp. 244–254
[10] Kozek AS (1990) A Nonparametric Test of Fit of a Linear Model.Communications in Statistics, Series A, 19:169–179 · Zbl 0900.62222 · doi:10.1080/03610929008830195
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