Second-derivative functional regression with applications to near infra-red spectroscopy

• 成果类型: Article
• 署名作者: Goutis, C
• 署名单位: Universidad Carlos III de Madrid
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/1467-9868.00111
• 发表日期: 1998
• 页码: 103-114
• 关键词: Nonparametric regression; statistical view; bandwidth choice; tools; differentiation; calibration; CURVES

摘要

A linear regression method to predict a scalar from a discretized smooth function is presented. The method takes into account the functional nature of the predictors and the importance of the second derivative in spectroscopic applications. This motivates a functional inner product that can be used as a roughness penalty. Using this inner product, we derive a linear prediction method that is similar to ridge regression but with different shrinkage characteristics. We describe its practical implementation and we address the problem of computing the second derivatives nonparametrically. We apply the method to a calibration example using near infra-red spectra. We conclude with a discussion comparing our approach with other regression algorithms.