估计员
花键(机械)
平滑的
平滑样条曲线
应用数学
数学
数学优化
一致性(知识库)
计算机科学
非线性系统
渐近分布
算法
人工智能
样条插值
统计
结构工程
量子力学
物理
工程类
双线性插值
作者
Guangyu Yang,Baqun Zhang,Min Zhang
标识
DOI:10.1080/01621459.2021.1947307
摘要
The linear spline model is able to accommodate nonlinear effects while allowing for an easy interpretation. It has significant applications in studying threshold effects and change-points. However, its application in practice has been limited by the lack of both rigorously studied and computationally convenient method for estimating knots. A key difficulty in estimating knots lies in the nondifferentiability. In this article, we study influence functions of regular and asymptotically linear estimators for linear spline models using the semiparametric theory. Based on the theoretical development, we propose a simple semismooth estimating equation approach to circumvent the nondifferentiability issue using modified derivatives, in contrast to the previous smoothing-based methods. Without relying on any smoothing parameters, the proposed method is computationally convenient. To further improve numerical stability, a two-step algorithm taking advantage of the analytic solution available when knots are known is developed to solve the proposed estimating equation. Consistency and asymptotic normality are rigorously derived using the empirical process theory. Simulation studies have shown that the two-step algorithm performs well in terms of both statistical and computational properties and improves over existing methods. Supplementary materials for this article are available online.
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