esag.mle: MLE of the ESAG distribution

In Directional: A Collection of Functions for Directional Data Analysis

MLE of the ESAG distribution

Description

MLE of the ESAG distribution.

Usage

esag.mle(y, full = FALSE, tol = 1e-06)
ESAGd.mle(y, full = FALSE)

Arguments

y	A matrix with the data expressed in Euclidean coordinates, i.e. unit vectors. The function esag.mle() works for spherical data, whereas ESAGd.mle() is for spherical and hyper-spherical data.
full	If you want some extra information, the inverse of the covariance matrix, the rho parameter (smallest eigenvalue of the covariance matrix) and the angle of rotation \psi, set this equal to TRUE. Otherwise leave it FALSE.
tol	A tolerance value to stop performing successive optimizations.

Details

MLE of the MLE of the ESAG distributiontribution, on the sphere, is implemented. ESAG stands for Elliptically Symmetric Angular Gaussian and it was suugested by Paine et al. (2018). Unlike the projected normal distribution this is rotationally symmetric and is a competitor of the spherical Kent distribution (which is also elliptically symmetric). ESAG was then generalized to arbitrary dimensions by Yu and Huang (2024).

Value

A list including:

mu	The mean vector.
gam	The \gamma parameters.
loglik	The log-likelihood value.
vinv	The inverse of the covariance matrix. It is returned if the argument "full" is TRUE.
rho	The \rho parameter (smallest eigenvalue of the covariance matrix). It is returned if the argument "full" is TRUE in the esag.mle().
psi	The angle of rotation \psi set this equal to TRUE. It is returned if the argument "full" is TRUE in esag.mle().
lambda	The d-1 eigenvalues of the covariance matrix of the ESAG distribution in arbitrary dimensions. This is returned if "full" is set to TRUE in the ESAGd.mle().
iag.loglik	The log-likelihood value of the isotropic angular Gaussian distribution in the esag.mle(). That is, the projected normal distribution which is rotationally symmetric.

Author(s)

Michail Tsagris and Zehao Yu.

R implementation and documentation: Michail Tsagris [e-mail] and Zehao Yu [e-mail].

References

Zehao Yu and Xianzheng Huang (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statististics, 18(1): 301–334.

Paine P.J., Preston S.P., Tsagris M. and Wood A.T.A. (2018). An Elliptically Symmetric Angular Gaussian Distribution. Statistics and Computing, 28(3):689–697.

Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

See Also

desag, resag, iag.mle, kent.mle, acg.mle, circ.summary, sphereplot

Examples

m <- colMeans( as.matrix( iris[, 1:3] ) )
y <- resag(1000, m, c(1, 0.5) )
esag.mle(y)

m <- colMeans( as.matrix( iris[, 1:4] ) )
y <- rESAGd(1000, m, c(1, 0.5, -1, 1, -0.5) )
ESAGd.mle(y)

Directional documentation built on Oct. 30, 2024, 9:15 a.m.