期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 112, 期 519, 页码 1261-1273出版社
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2016.1208615
关键词
Convergence rate; Differentiable manifold; Geometry; Local regression; Object data; Shape statistics
资金
- NSF [IIS1546331, SES-1357666, DMS-1407655, DMS-1127914]
- NIH [MH086633, 1UL1TR001111]
- Cancer Prevention Research Institute of Texas
- NATIONAL CANCER INSTITUTE [P30CA016672] Funding Source: NIH RePORTER
- NATIONAL CENTER FOR ADVANCING TRANSLATIONAL SCIENCES [UL1TR001111] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES [R01ES017240] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF MENTAL HEALTH [R01MH086633] Funding Source: NIH RePORTER
- Direct For Computer & Info Scie & Enginr [1663870] Funding Source: National Science Foundation
We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging, and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling iid manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient, and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples is considered indicating the wide applicability of our approach. Supplementary materials for this article are available online.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据