Some properties of a Cauchy family on the sphere derived from the Möbius transformations
From MaRDI portal
Publication:2203637
DOI10.3150/20-BEJ1222zbMath1455.60032arXiv1510.07679OpenAlexW3082690997MaRDI QIDQ2203637
Publication date: 7 October 2020
Published in: Bernoulli (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1510.07679
von Mises-Fisher distributionstereographic projectiondirectional statisticshigh dimensional datawrapped Cauchy distribution
Geometric probability and stochastic geometry (60D05) Exact distribution theory in statistics (62E15) Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05)
Related Items
Exponential-Wrapped Distributions on Symmetric Spaces, Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling, Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution, Recent advances in directional statistics, Density estimation for spherical data using nonparametric mixtures, Efficient sampling from the PKBD distribution, On synchronization in Kuramoto models on spheres, Consecutive ratios in second-order linear recurrence sequences
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Exact risk improvement of bandwidth selectors for kernel density estimation with directional data
- Möbius deconvolution on the hyperbolic plane with application to impedance density estimation
- Global maxima of real-valued functions
- Seul le groupe des similitudes-inversions préserve le type de la loi de Cauchy-conforme de \({\mathbb{R}}^ n\) pour \(n>1\). (Only the group of similitude-inversions preserves the Cauchy-conformal type distributions of \({\mathbb{R}}^ n\) for \(n>1)\)
- Une caractérisation du type de la loi de Cauchy-conforme sur \({\mathbb{R}}^ n\). (A characterization of the type of the conformal Cauchy law on \({\mathbb{R}}^ n)\)
- A family of distributions related to the McCullagh family
- Large sample theory of intrinsic and extrinsic sample means on manifolds. I
- Möbius transformation and Cauchy parameter estimation
- Asymptotic behavior of sample mean location for manifolds
- Skew-rotationally-symmetric distributions and related efficient inferential procedures
- Inference on the mode of weak directional signals: a Le Cam perspective on hypothesis testing near singularities
- Testing uniformity on high-dimensional spheres against monotone rotationally symmetric alternatives
- A possibly asymmetric multivariate generalization of the Möbius distribution for directional data
- The Möbius distribution on the disc
- The EM Algorithm and Extensions, 2E
- Some Statistical Properties of a Family of Continuous Univariate Distributions
- Conditional inference and Cauchy models
- Circular regression
- Tests of Concentration for Low-Dimensional and High-Dimensional Directional Data
- A Markov Process for Circular Data
- Foundations of Hyperbolic Manifolds
- A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation
- A Möbius transformation-induced distribution on the torus
- Distribution of the Serial Correlation Coefficient in a Circularly Correlated Universe
- Spherical regression