vmfkde.tune

Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (hyper-)spherical data whit cross validation.

 kernel density estimate 

 von Mises-Fisher distribution 

 Tuning of the bandwidth 

Tuning of the bandwidth parameter in the von Mises-Fisher kernel

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

Tuning of the bandwidth parameter in the von Mises-Fisher kernel function

<dl> <dt>x</dt>
<dd>A matrix with the data in Euclidean cordinates, i.e. unit vectors.</dd> <dt>low</dt>
<dd>The lower value of the bandwdith to search.</dd> <dt>up</dt>
<dd>The upper value of the bandwdith to search.</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

Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (hyper-)spherical data — Tuning of the bandwidth parameter in the von Mises-Fisher kernel

<dl>

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

 <dt>low</dt>
<dd>The lower value of the bandwdith to search.</dd>

 <dt>up</dt>
<dd>The upper value of the bandwdith to search.</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;.

Tuning of the bandwidth parameter in the von Mises-Fisher kernel: Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (hyper-)spherical data

Description

Usage

Value

Arguments

Author

Details

References

See Also

Examples