Generalized parametric help in Hilbertian additive regression

Pub Date : 2024-07-30 DOI:10.1007/s42952-024-00283-2
Seung Hyun Moon, Young Kyung Lee, Byeong U. Park
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Abstract

This paper introduces a powerful bias reduction technique applied to local linear additive regression. The main idea is to make use of a parametric family. Existing techniques based on this idea use a parametric model that is linear in the parameter. In this paper we generalize the approaches by allowing nonlinear parametric families. We develop the methodology and theory for response variables taking values in a general separable Hilbert space. Under mild conditions, our proposed approach not only offers flexibility but also gains bias reduction while maintaining the variance of the local linear additive regression estimators. We also provide numerical evidences that support our approach.

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希尔伯特加法回归中的广义参数帮助
本文介绍了一种应用于局部线性加法回归的强大的减少偏差技术。其主要思想是利用参数族。基于这一思想的现有技术使用的参数模型是参数的线性模型。在本文中,我们通过允许使用非线性参数族来推广这些方法。我们开发了在一般可分离希尔伯特空间取值的响应变量的方法和理论。在温和的条件下,我们提出的方法不仅具有灵活性,还能在保持局部线性加法回归估计方差的同时减少偏差。我们还提供了支持我们方法的数字证据。
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