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Estimating the error distribution function in nonparametric regression with multivariate covariates

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  • Müller, Ursula U.
  • Schick, Anton
  • Wefelmeyer, Wolfgang

Abstract

We consider nonparametric regression models with multivariate covariates and estimate the regression curve by an undersmoothed local polynomial smoother. The resulting residual-based empirical distribution function is shown to differ from the error-based empirical distribution function by the density times the average of the errors, up to a uniformly negligible remainder term. This result implies a functional central limit theorem for the residual-based empirical distribution function.

Suggested Citation

  • Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2009. "Estimating the error distribution function in nonparametric regression with multivariate covariates," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 957-964, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:957-964
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    Cited by:

    1. Györfi László & Walk Harro, 2013. "Rate of convergence of the density estimation of regression residual," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 55-74, March.
    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. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2014. "Testing for additivity in partially linear regression with possibly missing responses," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 51-61.
    4. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Chown, Justin, 2016. "Efficient estimation of the error distribution function in heteroskedastic nonparametric regression with missing data," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 31-39.
    6. Neumeyer, Natalie & Omelka, Marek & Hudecová, Šárka, 2019. "A copula approach for dependence modeling in multivariate nonparametric time series," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 139-162.

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