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Goodness-of-fit tests for the error distribution in nonparametric regression

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  • Heuchenne, Cédric
  • Van Keilegom, Ingrid

Abstract

Suppose the random vector (X,Y) satisfies the regression model Y=m(X)+[sigma](X)[epsilon], where m([dot operator]) is the conditional mean, [sigma]2([dot operator]) is the conditional variance, and [epsilon] is independent of X. The covariate X is d-dimensional (d>=1), the response Y is one-dimensional, and m and [sigma] are unknown but smooth functions. Goodness-of-fit tests for the parametric form of the error distribution are studied under this model, without assuming any parametric form for m or [sigma]. The proposed tests are based on the difference between a nonparametric estimator of the error distribution and an estimator obtained under the null hypothesis of a parametric model. The large sample properties of the proposed test statistics are obtained, as well as those of the estimator of the parameter vector under the null hypothesis. Finally, the finite sample behavior of the proposed statistics, and the selection of the bandwidths for estimating m and [sigma] are extensively studied via simulations.

Suggested Citation

  • Heuchenne, Cédric & Van Keilegom, Ingrid, 2010. "Goodness-of-fit tests for the error distribution in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1942-1951, August.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:8:p:1942-1951
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    References listed on IDEAS

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    11. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
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    Cited by:

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    2. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    3. J. Hambuckers & C. Heuchenne, 2017. "A robust statistical approach to select adequate error distributions for financial returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 137-161, January.
    4. M. Jiménez Gamero, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 412-413, September.

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