vmf.kde

A von Mises-Fisher kernel is used for the non parametric density estimation.

 kernel density estimate 

 von Mises-Fisher 

von Mises-Fisher kernel density estimation for (hyper-)spherical data

A collection of functions for directional data (including massive data, with millions of observations) analysis.
Hypothesis testing, discriminant and regression analysis, MLE of distributions and more are included.
The standard textbook for such data is the "Directional Statistics" by Mardia, K. V. and Jupp, P. E. (2000).
Other references include:
a) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (2018). "An elliptically symmetric angular Gaussian distribution". Statistics and Computing 28(3): 689-697. <doi:10.1007/s11222-017-9756-4>.
b) Tsagris M. and Alenazi A. (2019). "Comparison of discriminant analysis methods on the sphere". Communications in Statistics: Case Studies, Data Analysis and Applications 5(4):467--491. <doi:10.1080/23737484.2019.1684854>.
c) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (2020). "Spherical regression models with general covariates and anisotropic errors". Statistics and Computing 30(1): 153--165. <doi:10.1007/s11222-019-09872-2>.
d) Tsagris M. and Alenazi A. (2024). "An investigation of hypothesis testing procedures for circular and spherical mean vectors". Communications in Statistics-Simulation and Computation, 53(3): 1387--1408. <doi:10.1080/03610918.2022.2045499>.
e) Yu Z. and Huang X. (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statistics, 18(1): 301--334. <doi:10.1214/23-EJS2210>.
f) Tsagris M. and Alzeley O. (2024). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". Australian & New Zealand Journal of Statistics (Accepted for publication). <doi:10.48550/arXiv.2302.02468>.
g) Tsagris M., Papastamoulis P. and Kato S. (2024). "Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution". <doi:10.48550/arXiv.2409.03292>.

Michail Tsagris

Directional

A Collection of Functions for Directional Data Analysis

Giorgos Athineou

Christos Adam

Zehao Yu

Anamul Sajib

Eli Amson

Panagiotis Papastamoulis

von Mises-Fisher kernel density estimation for (hyper-)spherical data function

<dl><dt>x</dt>
<dd>A matrix with unit vectors, i.e. the data being expressed in Euclidean cordinates.</dd><dt>h</dt>
<dd>The bandwidth to be used.</dd><dt>thumb</dt>
<dd>If this is "none", the given bandwidth is used. If it is "rot" the rule of thumb suggested by Garcia-Portugues (2013) is used.</dd></dl>

Arguments

Michail Tsagris.
R implementation and documentation: Michail Tsagris <a href="/link/mtsagris%40uoc.gr?package=Directional&version=7.0" data-mini-rdoc="Directional::mtsagris@uoc.gr">mtsagris@uoc.gr</a> and Giorgos Athineou &lt;gioathineou@gmail.com&gt;.

Author

Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel — von Mises-Fisher kernel density estimation for (hyper-)spherical data

<dl>

<dt>x</dt>
<dd>A matrix with unit vectors, i.e. the data being expressed in Euclidean cordinates.</dd>

<dt>h</dt>
<dd>The bandwidth to be used.</dd>

<dt>thumb</dt>
<dd>If this is "none", the given bandwidth is used. If it is "rot" the rule of thumb suggested by Garcia-Portugues (2013) is used.</dd>

</dl>

Michail Tsagris.
R implementation and documentation: Michail Tsagris <a href='mailto:mtsagris@uoc.gr'>mtsagris@uoc.gr</a> and Giorgos Athineou &lt;gioathineou@gmail.com&gt;.

von Mises-Fisher kernel density estimation for (hyper-)spherical data: Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel

Description

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Arguments

Author

Details

References

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Examples