Some Stabilized Bandwidth Selectors for Nonparametric Regression
非参数回归中的稳定化带宽选择方法AI 解读 ↓
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非参数回归中的稳定化带宽选择方法
- 研究问题
- 研究非参数核回归的经典带宽选择为何具有较大的样本变动，以及能否通过稳定残差平方和改善选择精度和收敛速度。
- 方法与思路
- 作者从残差平方和的频域表示分析变动来源，通过修改观测的周期图稳定该准则，再替换经典选择器中的残差平方和。
- 材料陈述的贡献
- 摘要称稳定化带宽强一致，充分光滑时渐近正态且相对收敛速度达到参数速度，并报告模拟中优于经典选择器。
- 阅读关注点
- 应核对周期图修改方式、回归函数光滑性和适用设计，以及速度比较与模拟优势所依赖的具体限制条件。
- 阅读边界
- 仅依据版本未注明的 OpenAlex 索引摘要；作者明确指出情形较受限，未提供模拟数值，不能概括为普遍改善。
原文摘要
The problem of bandwidth selection for nonparametric kernel regression is considered. It is well recognized that the classical bandwidth selectors are subject to large sample variation. Due to the large variation, these selectors might not be very useful in practice. Based on the frequency-domain representation of the residual sum of squares (RSS), the source of the variation is pointed out. The observation leads to consideration of a procedure which stabilizes the RSS by modifying the periodogram of the observations. The stabilized bandwidth selectors are obtained by substituting the stabilized RSS for the RSS in the classical selectors. The strong consistency of the stabilized bandwidth estimate is established. For sufficiently smooth regression functions, it is shown that the stabilized bandwidth is asymptotically normal, and the relative convergence rate of the stabilized bandwidth estimate is $T^{-1/2}$ instead of the rate $T^{-1/10}$ of the classical estimates. In a simulation study, it is confirmed that the stabilized selectors perform much better than the classical selectors. The simulation results are consistent with the theoretic results. The article contains the important message that the commonly used cross-validation can be improved substantially. The procedure and the theoretic results are developed for a rather restrictive case. Further studies are required for more general situations.