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

Sheng-Yan Hong

Journal of Multivariate Analysis, 2002, vol. 80, issue 1, 1-20

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.

Keywords: bandwidth; choice; Berry-Esseen; rate; bias; reduction; data-driven; estimator; normal; approximation; semiparametric; regression; model (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (1)

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