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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.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
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| Colección: | Institute of Mathematical Statistics monographs.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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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) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Institute of Mathematical Statistics Monographs ; |v v. 2 | |
| 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. | |
| 500 | |a 9.3 Asymptotic distribution of the sample extrinsic mean. | ||
| 520 | |a A systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 229-234) and index. | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Nonparametric statistics. | |
| 650 | 0 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Mathematical statistics. | |
| 650 | 4 | |a Probabilities. | |
| 650 | 4 | |a Sequences (Mathematics) | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Nonparametric statistics. | |
| 650 | 6 | |a Statistique non paramétrique. | |
| 650 | 6 | |a Variétés (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Manifolds (Mathematics) |2 fast | |
| 650 | 7 | |a Nonparametric statistics |2 fast | |
| 700 | 1 | |a Bhattacharya, Rabi. | |
| 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. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=438982 |z Texto completo |
| 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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