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Dette, Holger; Munk, Axel; Wagner, Thorsten

Testing model assumptions in multivariate linear regression models. (English) Zbl 1033.62037

J. Nonparametric Stat. 12, No. 3, 309-342 (2000).
Summary: In the multivariate nonparametric regression model \(Y=g(t) +\varepsilon\) the problem of testing linearity of the regression function \(g\) and homoscedasticity of the distribution of the error \(\varepsilon\) is considered. For both problems a simple test is derived which is based on estimating the \(L^2\)-distance between the model space and the space induced by the hypothesis. The resulting statistics can be shown to be asymptotically normal, even under fixed alternatives. This extends and unifies recent results of H. Dette and A. Munk [Ann. Stat. 26, 778–800 (1998; Zbl 0930.62041); J. R. Stat. Soc., Ser. B 60, 693–708 (1998; Zbl 0909.62035)] to the multivariate case. A small simulation study on the finite sample behaviour of the proposed tests is reported and their properties are illustrated by analyzing a data example.

Cited in 3 Documents

MSC:

62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing

Keywords:

multivariate linear models; regression check; \(L^2\)-distance; homoscedastic errors; \(m\)-dependent random variables

Citations:

Zbl 0930.62041; Zbl 0909.62035

Software:

bootstrap
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Full Text: DOI

References:

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