Normal Approximation Rate and Bias Reduction for Data-Driven Kernel Smoothing Estimator in a Semiparametric Regression Model
✍ Scribed by Sheng-Yan Hong
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 168 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0047-259X
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✦ Synopsis
Accuracy of the normal approximation for Speckman's kernel smoothing estimator of the parametric component ; in the semiparametric regression model y=x { ;+ 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' C L criterion. We find that, contrary to what we might expect, this data-driven estimator cannot attain the optimal Berry Esseen rate n &1Â2 . Consequently, the confidence region of ; 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.