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Normal Approximation Rate and Bias Reduction for Data-Driven Kernel Smoothing Estimator in a Semiparametric Regression Model

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  • Hong, Sheng-Yan

Abstract

Accuracy of the normal approximation for Speckman's kernel smoothing estimator of the parametric component [beta] in the semiparametric regression model y=x[tau][beta]+g(t)+e is studied when the bandwidth used in the estimator is selected by a general data-based method which includes such commonly used bandwidth selectors as (delete-one-out) CV, GCV, and Mallows' CL criterion. We find that, contrary to what we might expect, this data-driven estimator cannot attain the optimal Berry-Esseen rate n-1/2. Consequently, the confidence region of [beta] based on this normal approximation is not first-order accurate. The reason for this is that the bias of Speckman's estimator is still of nonparametric order at the data-driven bandwidth choice. We then propose a resmoothing method to reduce the bias and show that the proposed estimator can achieve the optimal Berry-Esseen rate. A simulation study shows a slightly better small-sample performance of the proposed estimator.

Suggested Citation

  • Hong, Sheng-Yan, 2002. "Normal Approximation Rate and Bias Reduction for Data-Driven Kernel Smoothing Estimator in a Semiparametric Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 1-20, January.
    • Handle: RePEc:eee:jmvana:v:80:y:2002:i:1:p:1-20
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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    3. Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-680, May.
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    Cited by:

    1. You, Jinhong & Zhou, Xian & Zhou, Yong, 2010. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1079-1101, May.

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