Nonparametric Statistical Methods on Manifolds

Dryden, Ian L.; Le, Huiling; Preston, Simon P.; Wood, Andrew T. A.

Abstract

One of the many fundamental contributions that Rabi Bhattacharya, together with his coauthors, has made is the development of a general nonparametric theory of statistical inference on manifolds, in particular related to both intrinsic and extrinsic Fréchet means of probability distributions thereon (cf. Bhattacharya and Bhattacharya 2012, Bhattacharya, Patrangenaru 2013 and 2005). With the increasing importance of statistical analysis for non-Euclidean data in many applications, there is much scope for further advances related to this particular broad area of research. In the following, we concentrate on two particular important themes in data analysis on manifolds: nonparametric bootstrap methods and nonparametric curve fitting.

Citation

Dryden, I. L., Le, H., Preston, S. P., & Wood, A. T. A. (2016). Nonparametric Statistical Methods on Manifolds. In M. Denker, & E. C. Waymire (Eds.), Rabi N. Bhattacharya: Selected Papers (587-597). Springer. https://doi.org/10.1007/978-3-319-30190-7_17

• Online Publication Date: Jul 1, 2016
• Publication Date: 2016
• Deposit Date: Mar 25, 2021
• Publicly Available Date: Mar 26, 2021
• Publisher: Springer
• Pages: 587-597
• Series Title: Contemporary Mathematicians
• Book Title: Rabi N. Bhattacharya: Selected Papers
• ISBN: 9783319301884
• DOI: https://doi.org/10.1007/978-3-319-30190-7_17
• Public URL: https://nottingham-repository.worktribe.com/output/5415928
• Publisher URL: https://link.springer.com/chapter/10.1007/978-3-319-30190-7_17