Single and multiple index functional regression models with nonparametric link
具有非参数连接函数的单指标与多指标函数型回归AI 解读 ↓
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具有非参数连接函数的单指标与多指标函数型回归
- 研究问题
- 如何在函数型预测变量的回归中增加非线性表达能力，同时避免完全非参数估计过慢的收敛，是本文关注的问题。
- 方法与思路
- 作者提出非参数估计连接函数的新技术，并用自适应定义的函数型数据线性投影建立多指标模型。
- 材料陈述的贡献
- 摘要称该方法可实现具有多项式收敛速度的预测，并通过模拟与一个函数型回归应用考察有限样本表现。
- 阅读关注点
- 应核对连接函数与投影方向的估计步骤、指标数的选择、预测误差的定义，以及多项式速度所需条件。
- 阅读边界
- 材料为稿件版本未注明的 OpenAlex 索引摘要；未给出具体收敛指数、完整条件或应用结果，不能推断刊本差异。
原文摘要
Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional functions. This difficulty has led to an emphasis on the so-called functional linear model, which is much more flexible than common linear models in finite dimension, but nevertheless imposes structural constraints on the relationship between predictors and responses. Recent advances have extended the linear approach by using it in conjunction with link functions, and by considering multiple indices, but the flexibility of this technique is still limited. For example, the link may be modeled parametrically or on a grid only, or may be constrained by an assumption such as monotonicity; multiple indices have been modeled by making finite-dimensional assumptions. In this paper we introduce a new technique for estimating the link function nonparametrically, and we suggest an approach to multi-index modeling using adaptively defined linear projections of functional data. We show that our methods enable prediction with polynomial convergence rates. The finite sample performance of our methods is studied in simulations, and is illustrated by an application to a functional regression problem.