Nonparametric inference on manifolds : with applications to shape spaces / Abhishek Bhattacharya, Rabi Bhattacharya.

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.

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.

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.

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.

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.

9.3 Asymptotic distribution of the sample extrinsic mean.

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

Print version record.

Includes bibliographical references (pages 229-234) and index.

English.

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