.png){kind=icon}
返回
NONLINEAR SUFFICIENT DIMENSION REDUCTION FOR FUNCTIONAL DATA
.png){kind=icon}
OA
AI
DOI：10.1214/16-AOS1475.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
We propose a general theory and the estimation procedures for nonlinear sufficient dimension reduction where both the predictor and the response may be random functions. The relation between the response and predictor can be arbitrary and the sets of observed time points can vary from subject to subject. The functional and nonlinear nature of the problem leads to construction of two functional spaces: the first representing the functional data, assumed to be a Hilbert space, and the second characterizing nonlinearity, assumed to be a reproducing kernel Hilbert space. A particularly attractive feature of our construction is that the two spaces are nested, in the sense that the kernel for the second space is determined by the inner product of the first. We propose two estimators for this general dimension reduction problem, and establish the consistency and convergence rate for one of them. These asymptotic results are flexible enough to accommodate both fully and partially observed functional data. We investigate the performances of our estimators by simulations, and applied them to data sets about speech recognition and handwritten symbols.
Keyword:
Convergence rate
linear operator
handwriting data
reproducing kernel Hilbert space
speech recognition
Sliced Average Variance Estimator
Sliced Inverse Regression
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
3.7
论文数:
2.8K
被引数:
2.9W
机构
引用论文
.png){kind=icon}
分享收藏
查看更多内容