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Testing the hypothesis of a general linear model using nonparametric regression estimation

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Summary

Given the modelY i =m(χ i )+ɛi,whereE(ɛ i) =0,X i ≠Ci=1, ...,n, andC is ap-dimensional compact set, we have designed a new method for testing the hypothesis that the regression function follows a general linear model,m(·) ∈ {m θ(·) =A t(·)θ}θ∈Θ⊂ℛq , withA a function fromℜ p toℜ q. The statistic, denoted ΔASE, used fortesting the given hypothesis is defined to be the difference between the average squared errors (ASE) associated with the non-parametric estimator\(\hat m\) ofm and the minimum distance parametric estimator\(m_{\hat \theta } \) ofm. The asymptotic normality of both ΔASE and the minimum distance estimators is proved under general conditions. Alternative bootstrap versions of ΔASE are also considered.

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad de Santiago de Compostela, 15771, Santiago de Compostela, Spain

    W. González-Manteiga & R. Cao

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  1. W. González-Manteiga
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  2. R. Cao
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González-Manteiga, W., Cao, R. Testing the hypothesis of a general linear model using nonparametric regression estimation. Test 2, 161–188 (1993). https://doi.org/10.1007/BF02562674

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