标题： 带有稀疏设计的数据的微分方程约束局部回归 显示英文标题

标题： Differential Equation-Constrained Local Regression for Data with Sparse Design

摘要： 一阶或更高阶的局部多项式回归在数据稀疏的区域通常表现不佳。 相反，局部常数回归在这些区域往往更稳健，尽管它通常是最不准确的方法，尤其是在数据边界附近。 纳入可能近似或精确成立的微分方程的信息，是一种在保持局部常数回归稀疏设计能力的同时减少偏差和方差的方法。 本文研究了一种利用一阶微分方程的非参数回归方法，并将其应用于噪声老鼠肿瘤生长数据。 讨论了使用不同次数泰勒多项式的核估计量的渐近偏差和方差。 通过模拟研究，在模拟指数型增长的各种场景下进行了模型比较。 显示英文摘要

摘要： Local polynomial regression of order one or higher often performs poorly in areas with sparse data. In contrast, local constant regression tends to be more robust in these regions, although it is generally the least accurate approach, especially near the boundaries of the data. Incorporating information from differential equations, which may approximately or exactly hold, is one way of extending the sparse design capacity of local constant regression while reducing bias and variance. A nonparametric regression method that exploits first-order differential equations is studied in this paper and applied to noisy mouse tumour growth data. Asymptotic biases and variances of kernel estimators using Taylor polynomials with different degrees are discussed. Model comparison is performed for different estimators through simulation studies under various scenarios that simulate exponential-type growth.