Diffusion means in geometric spaces

Cites Work

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Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth
Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
Simulation of conditioned diffusion and application to parameter estimation
On the parabolic kernel of the Schrödinger operator
Generalized Procrustes analysis
Mean location and sample mean location on manifolds: Asymptotics, tests, confidence regions
Large sample theory of intrinsic and extrinsic sample means on manifolds. I
Bootstrapping descriptors for non-Euclidean data
Backward nested descriptors asymptotics with inference on stem cell differentiation
Asymptotic behavior of sample mean location for manifolds
The statistical theory of shape
On the meaning of mean shape: manifold stability, locus and the two sample test
Barycentric subspace analysis on manifolds
Geometrical smeariness -- a new phenomenon of Fréchet means
The Stein effect for Fréchet means
Smeariness begets finite sample smeariness
Diffusion means and heat kernel on manifolds
Intrinsic means on the circle: uniqueness, locus and asymptotics
A smeary central limit theorem for manifolds with application to high-dimensional spheres
Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry
Large sample theory of intrinsic and extrinsic sample means on manifolds. II.
Pointwise monotonicity of heat kernels
Barycentric Subspaces and Affine Spans in Manifolds
Statistical shape analysis. With applications in R
Inference on 3D Procrustes means: tree bole growth, rank deficient diffusion tensors and perturbation models
Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
The Heat Kernel on Hyperbolic Space
On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
Riemannian center of mass and mollifier smoothing
The Fréchet mean shape and the shape of the means
Mean Figures and Mean Shapes Applied to Biological Figure and Shape Distributions in the Plane
References
Strong laws of large numbers for generalizations of Fréchet mean sets
Extrinsic Mean of Brownian Distributions on Compact Lie Groups
Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups
Principal component analysis and the locus of the Fréchet mean in the space of phylogenetic trees
Extrinsic vs Intrinsic Means on the Circle
On the convergence of some Procrustean averaging algorithms
Theory of Random Sets
On the measure of the cut locus of a Fréchet mean
An Empirical Bayes Approach to Shrinkage Estimation on the Manifold of Symmetric Positive-Definite Matrices
Finite sample smeariness of Fréchet means with application to climate

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