An Invitation to Statistics in Wasserstein Space. - Panaretos, Victor M.; Zemel, Yoav. (Cham : Springer International Publishing AG, 2020)
3.2.1 Existence, Uniqueness, and Continuity -- 3.2.2 The One-Dimensional Case -- 3.2.3 Differentiability of the Population Fréchet Functional -- 3.3 Bibliographical Notes -- 4 Phase Variation and Fréchet Means -- 4.1 Amplitude and Phase Variation -- 4.1.1 The Functional Case -- 4.1.2 The Point Process Case -- 4.2 Wasserstein Geometry and Phase Variation -- 4.2.1 Equivariance Properties of the Wasserstein Distance -- 4.2.2 Canonicity of Wasserstein Distance in Measuring Phase Variation -- 4.3 Estimation of Fréchet Means -- 4.3.1 Oracle Case -- 4.3.2 Discretely Observed Measures -- 4.3.3 Smoothing -- 4.3.4 Estimation of Warpings and Registration Maps -- 4.3.5 Unbiased Estimation When X=R -- 4.4 Consistency -- 4.4.1 Consistent Estimation of Fréchet Means -- 4.4.2 Consistency of Warp Functions and Inverses -- 4.5 Illustrative Examples -- 4.5.1 Explicit Classes of Warp Maps -- 4.5.2 Bimodal Cox Processes -- 4.5.3 Effect of the Smoothing Parameter -- 4.6 Convergence Rates and a Central Limit Theoremon the Real Line -- 4.7 Convergence of the Empirical Measure and Optimality -- 4.8 Bibliographical Notes -- 5 Construction of Fréchet Means and Multicouplings -- 5.1 A Steepest Descent Algorithm for the Computation of FréchetMeans -- 5.2 Analogy with Procrustes Analysis -- 5.3 Convergence of Algorithm 1 -- 5.4 Illustrative Examples -- 5.4.1 Gaussian Measures -- 5.4.2 Compatible Measures -- 5.4.2.1 The One-Dimensional Case -- 5.4.2.2 Independence -- 5.4.2.3 Common Copula -- 5.4.3 Partially Gaussian Trivariate Measures -- 5.5 Population Version of Algorithm 1 -- 5.6 Bibliographical Notes -- References.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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