Nonparametric inference on manifolds : with applications to shape spaces /

A systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes.

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Online Access: Full text (MCPHS users only)
Main Author: Bhattacharya, Abhishek
Other Authors: Bhattacharya, Rabi
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 2012
Series:Institute of Mathematical Statistics monographs.
Subjects:
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100 1 |a Bhattacharya, Abhishek. 
245 1 0 |a Nonparametric inference on manifolds :  |b with applications to shape spaces /  |c Abhishek Bhattacharya, Rabi Bhattacharya. 
260 |a Cambridge :  |b Cambridge University Press,  |c 2012. 
300 |a 1 online resource (237 pages) 
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490 1 |a Institute of Mathematical Statistics Monographs ;  |v v. 2 
500 |a 9.3 Asymptotic distribution of the sample extrinsic mean. 
504 |a Includes bibliographical references (pages 229-234) and index. 
505 0 |a Cover; Nonparametric Inference on Manifolds; Title; Copyright; Contents; Commonly used notation; Preface; 1: Introduction; 2: Examples; 2.1 Data example on S1: wind and ozone; 2.2 Data examples on S2: paleomagnetism; 2.3 Data example on Sk2: shapes of gorilla skulls; 2.4 Data example on Sk2: brain scan shapes of schizophrenic and normal patients; 2.5 Data example on affine shape space ASk2: application to handwritten digit recognition; 2.6 Data example on reflection similarity shape space RSk3: glaucoma detection; 2.7 References; 3: Location and spread on metric spaces; 3.1 Introduction. 
505 8 |a 3.2 Location on metric spaces3.3 Variation on metric spaces; 3.4 Asymptotic distribution of the sample mean; 3.5 Asymptotic distribution of the sample variation; 3.6 An example: the unit circle; 3.7 Data example on S1; 3.8 References; 4: Extrinsic analysis on manifolds; 4.1 Extrinsic mean and variation; 4.2 Asymptotic distribution of the sample extrinsic mean; 4.3 Asymptotic distribution of the sample extrinsic variation; 4.4 Asymptotic joint distribution of the sample extrinsic mean and variation; 4.5 Two-sample extrinsic tests; 4.5.1 Independent samples; 4.5.2 Matched pair samples. 
505 8 |a 4.6 Hypothesis testing using extrinsic mean and variation4.6.1 Independent samples; 4.7 Equivariant embedding; 4.8 Extrinsic analysis on the unit sphere Sd; 4.9 Applications on the sphere; 4.9.1 Magnetization direction data; 4.9.2 Volcano Location Data; 4.10 References; 5: Intrinsic analysis on manifolds; 5.1 Intrinsic mean and variation; 5.2 Asymptotic distribution of the sample intrinsic mean; 5.3 Intrinsic analysis on Sd; 5.4 Two-sample intrinsic tests; 5.4.1 Independent samples; 5.4.2 Matched pair samples; 5.5 Data example on S2. 
505 8 |a 5.6 Some remarks on the uniqueness of the intrinsic mean and the nonsingularity of the asymptotic distribution of the sample mean5.7 References; 6: Landmark-based shape spaces; 6.1 Introduction; 6.2 Geometry of shape manifolds; 6.2.1 Similarity shape spaces Skm; 6.2.2 Reflection similarity shape spaces RSkm; 6.2.3 Affine shape spaces ASkm; 6.2.4 Projective shape spaces PSk; 6.3 References; 7: Kendall's similarity shape spaces Skm; 7.1 Introduction; 7.2 Geometry of similarity shape spaces; 7.3 References; 8: The planar shape space Sk2; 8.1 Introduction; 8.2 Geometry of the planar shape space. 
505 8 |a 8.3 Examples8.3.1 Gorilla skulls; 8.3.2 Schizophrenic patients; 8.4 Intrinsic analysis on the planar shape space; 8.5 Other Fréchet functions; 8.6 Extrinsic analysis on the planar shape space; 8.7 Extrinsic mean and variation; 8.8 Asymptotic distribution of the sample extrinsic mean; 8.9 Two-sample extrinsic tests on the planar shape space; 8.10 Planar size-and-shape manifold; 8.11 Applications; 8.11.1 Gorilla skulls; 8.11.2 Schizophrenia detection; 8.12 References; 9: Reflection similarity shape spaces RSkm; 9.1 Introduction; 9.2 Extrinsic analysis on the reflection shape space. 
520 |a A systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. 
546 |a English. 
588 0 |a Print version record. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Nonparametric statistics. 
650 0 |a Manifolds (Mathematics) 
700 1 |a Bhattacharya, Rabi. 
758 |i has work:  |a Nonparametric inference on manifolds (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGPGV8fKmVcDMWtWdqYvRC  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Bhattacharya, Abhishek.  |t Nonparametric Inference on Manifolds.  |d Cambridge : Cambridge University Press, 2012  |z 9781139338769 
830 0 |a Institute of Mathematical Statistics monographs. 
852 |b E-Collections  |h ProQuest 
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880 8 |6 505-00/(S  |a 8.3 Examples8.3.1 Gorilla skulls; 8.3.2 Schizophrenic patients; 8.4 Intrinsic analysis on the planar shape space; 8.5 Other Fréchet functions; 8.6 Extrinsic analysis on the planar shape space; 8.7 Extrinsic mean and variation; 8.8 Asymptotic distribution of the sample extrinsic mean; 8.9 Two-sample extrinsic tests on the planar shape space; 8.10 Planar size-and-shape manifold; 8.11 Applications; 8.11.1 Gorilla skulls; 8.11.2 Schizophrenia detection; 8.12 References; 9: Reflection similarity shape spaces RΣkm; 9.1 Introduction; 9.2 Extrinsic analysis on the reflection shape space. 
880 0 |6 505-00/(S  |a Cover; Nonparametric Inference on Manifolds; Title; Copyright; Contents; Commonly used notation; Preface; 1: Introduction; 2: Examples; 2.1 Data example on S1: wind and ozone; 2.2 Data examples on S2: paleomagnetism; 2.3 Data example on Σk2: shapes of gorilla skulls; 2.4 Data example on Σk2: brain scan shapes of schizophrenic and normal patients; 2.5 Data example on affine shape space AΣk2: application to handwritten digit recognition; 2.6 Data example on reflection similarity shape space RΣk3: glaucoma detection; 2.7 References; 3: Location and spread on metric spaces; 3.1 Introduction. 
880 8 |6 505-00/(S  |a 5.6 Some remarks on the uniqueness of the intrinsic mean and the nonsingularity of the asymptotic distribution of the sample mean5.7 References; 6: Landmark-based shape spaces; 6.1 Introduction; 6.2 Geometry of shape manifolds; 6.2.1 Similarity shape spaces Σkm; 6.2.2 Reflection similarity shape spaces RΣkm; 6.2.3 Affine shape spaces AΣkm; 6.2.4 Projective shape spaces PΣk; 6.3 References; 7: Kendall's similarity shape spaces Σkm; 7.1 Introduction; 7.2 Geometry of similarity shape spaces; 7.3 References; 8: The planar shape space Σk2; 8.1 Introduction; 8.2 Geometry of the planar shape space. 
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