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Bootstrap tests for the error distribution in linear and nonparametric regression models

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  • Nagel, Eva-Renate
  • Dette, Holger
  • Neumeyer, Natalie

Abstract

In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to deal with this problem. The performance of the resulting bootstrap test is investigated from an asymptotic point of view and by means of a simulation study. The results demonstrate that even for moderate sample sizes the parametric bootstrap provides a reliable and easy accessible solution to the problem of goodness-of-fit testing of assumptions regarding the error distribution in linear and nonparametric regression models.

Suggested Citation

  • Nagel, Eva-Renate & Dette, Holger & Neumeyer, Natalie, 2004. "Bootstrap tests for the error distribution in linear and nonparametric regression models," Technical Reports 2004,38, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200438
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    References listed on IDEAS

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    1. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    2. Koul, H. L. & Lahiri, S. N., 1994. "On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 255-265, May.
    3. Lepski, O. & Tsybakov, A., 1996. "Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point," SFB 373 Discussion Papers 1996,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Efromovich, Sam & Samarov, Alex, 1996. "Asymptotic equivalence of nonparametric regression and white noise model has its limits," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 143-145, June.
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    1. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Other publications TiSEM 0c6f2c43-aa7d-45c1-9d43-7, Tilburg University, School of Economics and Management.
    2. J. Baixauli & Susana Alvarez, 2006. "Evaluating effects of excess kurtosis on VaR estimates: Evidence for international stock indices," Review of Quantitative Finance and Accounting, Springer, vol. 27(1), pages 27-46, August.
    3. Einmahl, J.H.J. & van Keilegom, I., 2004. "Goodness-of-fit Tests in Nonparametric Regression," Other publications TiSEM 44e08f75-b35d-424e-b33e-0, Tilburg University, School of Economics and Management.

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