SMOOTHED EMPIRICAL LIKELIHOOD METHODS FOR QUANTILE REGRESSION MODELS
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分位数回归模型的平滑经验似然方法
- 研究问题
- 如何用经验似然估计分位数回归参数并改善置信区域的高阶覆盖精度，平滑与 Bartlett 修正分别起什么作用？
- 方法与思路
- 作者平滑经验似然的估计方程，研究估计量的一阶等价性和置信区域的高阶覆盖误差，并通过模拟比较方法。
- 材料陈述的贡献
- 摘要称估计量与标准分位数回归一阶渐近等价，覆盖误差为 n⁻¹ 阶，Bartlett 修正后可达 n⁻² 阶。
- 阅读关注点
- 核对平滑方式、带宽及高阶展开条件，查看 Bartlett 修正的计算方法，并审视与平滑 bootstrap 比较的模拟范围。
- 阅读边界
- 仅据所给 OpenAlex 摘要，高阶误差结论的完整条件未说明；模拟仅提示小样本精度可能改善，不能认定普遍优越。
原文摘要
This paper considers an empirical likelihood method to estimate the parameters of the quantile regression (QR) models and to construct confidence regions that are accurate in finite samples. To achieve the higher order refinements, we smooth the estimating equations for the empirical likelihood. We show that the smoothed empirical likelihood estimator is first-order asymptotically equivalent to the standard QR estimator and establish that confidence regions based on the smoothed empirical likelihood ratio have coverage errors of order n−1 and may be Bartlett corrected to produce regions with errors of order n−2, where n denotes the sample size. Our result is an extension of the previous result of Chen and Hall (1993, Annals of Statistics 21, 1166–1181) to the regression context. Monte Carlo experiments suggest that the smoothed empirical likelihood confidence regions may be more accurate in small samples than the confidence regions that can be constructed from the smoothed bootstrap method recently suggested by Horowitz (1998, Econometrica 66, 1327–1351).I thank the co-editor Bruce Hansen and anonymous referees for valuable suggestions and comments. I also thank Song X. Chen, Joel Horowitz, Yuichi Kitamura, Oliver Linton, Whitney Newey, Peter Phillips, and Richard Smith for helpful comments. Parts of this paper were written while I was visiting the Cowles Foundation at Yale University, whose hospitality is gratefully acknowledged. Young-Hyun Cho has provided excellent research assistance. This work was supported by the Korea Research Foundation grant KRF 2003-041-B00072.