Smooth backfitting for errors-in-variables additive models
含测量误差的加性模型的平滑回拟合AI 解读 ↓
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含测量误差的加性模型的平滑回拟合
- 研究问题
- 协变量受到测量误差污染时，如何估计加性非参数回归，并处理回拟合过程中误差向其他加性分量传播的问题？
- 方法与思路
- 作者设计兼具反卷积作用与加性函数空间投影解释的新核权重，并据此构造平滑回拟合估计量及其收敛理论。
- 材料陈述的贡献
- 摘要称，误差分布平滑度低于某阈值时达到一维反卷积最优速率；高于阈值时速率变慢，但仍快于多维最优速率。
- 阅读关注点
- 应核对平滑度阈值的定义、核函数构造、投影解释成立的条件，以及跨分量误差传播如何影响收敛速率和有限样本表现。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；摘要未给出阈值、具体速率及误差分布条件，有限样本比较也无数值结果。
原文摘要
In this work, we develop a new smooth backfitting method and theory for estimating additive nonparametric regression models when the covariates are contaminated by measurement errors. For this, we devise a new kernel function that suitably deconvolutes the bias due to measurement errors as well as renders a projection interpretation to the resulting estimator in the space of additive functions. The deconvolution property and the projection interpretation are essential for a successful solution of the problem. We prove that the method based on the new kernel weighting scheme achieves the optimal rate of convergence in one-dimensional deconvolution problems when the smoothness of measurement error distribution is less than a threshold value. We find that the speed of convergence is slower than the univariate rate when the smoothness of measurement error distribution is above the threshold, but it is still much faster than the optimal rate in multivariate deconvolution problems. The theory requires a deliberate analysis of the nonnegligible effects of measurement errors being propagated to other additive components through backfitting operation. We present the finite sample performance of the deconvolution smooth backfitting estimators that confirms our theoretical findings.