### Abstract

An expository account of the recent theory of nonparametric inference on manifolds is presented here, with outlines of proofs and examples. Much of the theory centers around Fréchet means; but functional estimation and classification methods using nonparametric Bayes theory are also indicated. Applications in paleomagnetism, morphometrics and medical diagnostics illustrate the theory.

Original language | English (US) |
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Title of host publication | Limit Theorems in Probability, Statistics and Number Theory |

Subtitle of host publication | In Honor of Friedrich Gotze |

Publisher | Springer New York LLC |

Pages | 173-205 |

Number of pages | 33 |

ISBN (Print) | 9783642360671 |

DOIs | |

State | Published - Jan 1 2013 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 42 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Keywords

- Fréchet mean
- extrinsic inference
- intrinsic inference
- shape spaces

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Bhattacharya, R. (2013). A nonparametric theory of statistics on manifolds. In

*Limit Theorems in Probability, Statistics and Number Theory: In Honor of Friedrich Gotze*(pp. 173-205). (Springer Proceedings in Mathematics and Statistics; Vol. 42). Springer New York LLC. https://doi.org/10.1007/978-3-642-36068-8_9