axialnntsmanifoldnewtonestimationgradientstop {CircNNTSRaxial} | R Documentation |
Parameter estimation for axial NNTS distributions with gradient stop
Description
Computes the maximum likelihood estimates of the parameters of an axial NNTS distribution, using a Newton algorithm on the hypersphere and considering a maximum number of iterations determined by a constraint in terms of the norm of the gradient
Usage
axialnntsmanifoldnewtonestimationgradientstop(data, M = 0, iter = 1000,
initialpoint = FALSE, cinitial,gradientstop=1e-10)
Arguments
data |
Vector of axial angles in radians |
M |
Number of components in the NNTS axial model |
iter |
Number of iterations |
initialpoint |
TRUE if an initial point for the optimization algorithm for the axial NNTS density will be used |
cinitial |
Vector of size M+1. The first element is real and the next M elements are complex (values for $c_0$ and $c_1, ...,c_M$). The sum of the squared moduli of the parameters must be equal to 1/pi. |
gradientstop |
The minimum value of the norm of the gradient to stop the Newton algorithm on the hypersphere |
Value
A list with 5 elements:
cestimates |
Matrix of (M+1)x2. The first column is the parameter numbers, and the second column is the c parameter's estimators of the NNTS axial model |
loglik |
Optimum log-likelihood value for the NNTS axial model |
AIC |
Value of Akaike's Information Criterion |
BIC |
Value of Bayesian Information Criterion |
gradnormerror |
Gradient error after the last iteration |
Author(s)
Juan Jose Fernandez-Duran and Maria Mercedes Gregorio-Dominguez
References
Fernandez-Duran, J.J. and Gregorio-Dominguez, M.M. (2025). Multimodal distributions for circular axial data. arXiv:2504.04681 [stat.ME] (available at https://arxiv.org/abs/2504.04681)
Fernández-Durán, J.J., Gregorio-Domínguez, M.M. (2025). Multimodal Symmetric Circular Distributions Based on Nonnegative Trigonometric Sums and a Likelihood Ratio Test for Reflective Symmetry, arXiv:2412.19501 [stat.ME] (available at https://arxiv.org/abs/2412.19501)
Examples
data(Datab2fisher)
feldsparsangles<-Datab2fisher$orientations
feldsparsangles<-feldsparsangles*(pi/180)
resfeldspars<-axialnntsmanifoldnewtonestimationgradientstop(data=feldsparsangles,
M = 2,iter=1000,gradientstop=1e-10)
resfeldspars