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Residuals density estimation in nonparametric regression

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  • Ahmad, Ibrahim A.

Abstract

For the fixed design regression model, a nonparametric estimate of the probability density function of the residuals is proposed and its basic properties are studied. This estimate should have direct impact on diagnostics of regression models of this type. The estimate proposed here is based on estimating the regression function at the regressor points thus giving estimates of the residuals. Then these residual estimators are used to construct a kernel estimate of residuals density. The estimate is shown, among other things, to be consistent and asymptotically normal.

Suggested Citation

  • Ahmad, Ibrahim A., 1992. "Residuals density estimation in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 133-139, May.
    • Handle: RePEc:eee:stapro:v:14:y:1992:i:2:p:133-139
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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. Devroye, Luc & Felber, Tina & Kohler, Michael & Krzyżak, Adam, 2012. "L1-consistent estimation of the density of residuals in random design regression models," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 173-179.
    4. Kengo Kato, 2012. "Asymptotic normality of Powell’s kernel estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 255-273, April.
    5. Nadine Hilgert & Bruno Portier, 2012. "Strong uniform consistency and asymptotic normality of a kernel based error density estimator in functional autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 15(2), pages 105-125, July.

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