Smoothing Spline Models with Correlated Random Errors
具有相关随机误差的平滑样条模型AI 解读 ↓
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具有相关随机误差的平滑样条模型
- 研究问题
- 当非参数回归观测具有相关误差时，如何同时估计样条平滑参数与相关参数，避免独立性方法造成平滑参数低估？
- 方法与思路
- 作者假定相关矩阵由少量参数描述，扩展GML、GCV和UBR以联合估计，并通过三个混合效应模型联系BLUP与REML。
- 材料陈述的贡献
- 摘要称给出通过SAS混合模型程序拟合的途径，并展示时间序列和空间数据应用；作者基于所做模拟推荐GML方法。
- 阅读关注点
- 应核对相关矩阵的参数化及可识别性、混合模型等价关系，并检查模拟中样本量、相关强度和各方法的调参实现。
- 阅读边界
- 仅据稿件版本未注明的OpenAlex索引摘要；模拟推荐受所用设计限制，相关结构误设时的表现及具体数值未说明。
原文摘要
Spline-smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model. Their performances depend greatly on the choice of smoothing parameters. Many methods of selecting smoothing parameters such as generalized maximum likelihood (GML), generalized cross-validation (GCV), and unbiased risk (UBR), have been developed under the assumption of independent observations. They tend to underestimate smoothing parameters when data are correlated. In this article, I assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters. I extend the GML, GCV, and UBR methods to estimate the smoothing parameters and the correlation parameters simultaneously. I also relate a smoothing spline model to three mixed-effects models. These relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction (BLUP) estimates and that the GML estimates of the smoothing parameters and the correlation parameters are restricted maximum likelihood (REML) estimates. They also provide a way to fit a spline model with correlated errors using the SAS procedure proc mixed. Simulations are conducted to evaluate and compare the performance of the GML, GCV, UBR methods and the method proposed by Diggle and Hutchinson. The GML method is recommended, because it is stable and works well in all simulations. It performs better than other methods, especially when the sample size is not large. I illustrate my methods with applications to time series data and to spatial data.