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Estimating the error distribution function in semiparametric regression

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  • Müller Ursula U.
  • Schick Anton
  • Wefelmeyer Wolfgang

Abstract

We prove a stochastic expansion for a residual-based estimator of the error distribution function in a partly linear regression model. It implies a functional central limit theorem. As special cases we cover nonparametric, nonlinear and linear regression models.

Suggested Citation

  • Müller Ursula U. & Schick Anton & Wefelmeyer Wolfgang, 2007. "Estimating the error distribution function in semiparametric regression," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-18, January.
    • Handle: RePEc:bpj:strimo:v:25:y:2007:i:1/2007:p:18:n:1
    DOI: 10.1524/stnd.2007.25.1.1
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    References listed on IDEAS

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    1. Kiwitt, Sebastian & Nagel, Eva-Renate & Neumeyer, Natalie, 2005. "Empirical likelihood estimators for the error distribution in nonparametric regression models," Technical Reports 2005,45, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. 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.
    3. Schick, Anton, 1996. "Root-n consistent estimation in partly linear regression models," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 353-358, August.
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    Cited by:

    1. Juan Mora & Alicia Pérez-Alonso, 2009. "Specification tests for the distribution of errors in nonparametric regression: a martingale approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 441-452.
    2. Györfi, László & Walk, Harro, 2012. "Strongly consistent density estimation of the regression residual," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1923-1929.
    3. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
    4. Neumeyer, Natalie, 2009. "Testing independence in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1551-1566, August.
    5. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    6. Justin Chown & Ursula U. Müller, 2013. "Efficiently estimating the error distribution in nonparametric regression with responses missing at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(3), pages 665-677, September.

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