A consistent test for the functional form of a regression based on a difference of variance estimators
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TLDR
In this article, a consistent test is proposed which is based on the difference of the least square variance estimator in the assumed regression model and a nonparametric estimator, and the corresponding test statistic can be shown to be asymptotically normal under the null hypothesis and under fixed alternatives with different rates of convergence corresponding to both cases.Abstract:
In this paper we study the problem of testing the functional form of a given regression model. A consistent test is proposed which is based on the difference of the least squares variance estimator in the assumed regression model and a nonparametric variance estimator. The corresponding test statistic can be shown to be asymptotically normal under the null hypothesis and under fixed alternatives with different rates of convergence corresponding to both cases. This provides a simple asymptotic test, where the asymptotic results can also be used for the calculation of the type II error of the procedure at any particular point of the alternative and for the construction of tests for precise hypotheses. Finally, the finite sample performance of the new test is investigated in a detailed simulation study, which also contains a comparison with the commonly used tests.read more
Citations
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References
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Design-adaptive Nonparametric Regression
TL;DR: In this paper, a weighted local linear regression (LR) was proposed for nonparametric regression, which has high asymptotic efficiency and adapts to both random and fixed designs, to both highly clustered and nearly uniform designs, and even to both interior and boundary points.
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Comparing Nonparametric Versus Parametric Regression Fits
Wolfgang Karl Härdle,Enno Mammen +1 more
TL;DR: In this paper, the wild bootstrap method was used to fit Engel curves in expenditure data analysis, and it was shown that the standard way of bootstrapping this statistic fails.
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Nonlinear Statistical Models
TL;DR: In this article, a Unified Asymptotic Theory for Nonlinear Regression with Regression Structure (UATRS) is proposed. But it is not a unified theory for dynamic nonlinear models.