axialnntsmanifoldnewtonestimationgradientstopknownmusymmetric: Parameter estimation for axial symmetric NNTS distributions...

In CircNNTSRaxial: Axial Data using NNTS Models

Parameter estimation for axial symmetric NNTS distributions with known location angle gradient stop

Description

Computes the maximum likelihood estimates of the parameters of an axial symmetric NNTS distribution with known location angle, 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

axialnntsmanifoldnewtonestimationgradientstopknownmusymmetric(data, muknown=0, M = 0, 
iter = 1000, initialpoint = FALSE, cinitial,gradientstop=1e-10)

Arguments

data	Vector of axial angles in radians
muknown	Value of the known location angle
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. This is the vector of parameters for the general (asymmetric) NNTS axial density
gradientstop	The minimum value of the norm of the gradient to stop the Newton algorithm on the hypersphere

Value

A list with 13 elements:

cestimatesmuknown	Matrix of (M+1)x2. The first column is the parameter numbers, and the second column is the c parameter's estimators of the symmetric NNTS axial model with known location angle
muknown	Known value of the location angle of the symmetric NNTS axial model
loglikmuknown	Optimum log-likelihood value for the symmetric NNTS axial model with known location angle
AICmuknown	Value of Akaike's Information Criterion for the symmetric NNTS axial model with known location angle
BICmuknown	Value of Bayesian Information Criterion for the symmetric NNTS axial model with known location angle
gradnormerrormuknown	Gradient error after the last iteration for the estimation of the parameters of the symmetric NNTS axial model with known location angle
cestimatesmuunknown	Matrix of (M+1)x2. The first column is the parameter numbers, and the second column is the c parameter's estimators of the general (non-symmetric) NNTS axial model with unknown location angle
loglikmuunknown	Optimum log-likelihood value for the general (non-symmetric) NNTS axial model with unknown location angle
AICmuunknown	Value of Akaike's Information Criterion for the general (non-symmetric) NNTS axial model with unknown location angle
BICmuunknown	Value of Bayesian Information Criterion for the general (non-symmetric) NNTS axial model with unknown location angle
gradnormerrormuunknown	Gradient error after the last iteration for the estimation of the parameters of the general (non-symmetric) NNTS axial model with unknown location angle
loglikratioformuknown	Value of the likelihood ratio test statistic for known location angle
loglikratioformuknownpvalue	Value of the asymptotic chi squared p-value of the likelihood ratio test statistic for known location angle

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
feldsparsangles<-feldsparsangles$orientations*(pi/180)
resfeldsparknownanglesymmetric<-axialnntsmanifoldnewtonestimationgradientstopknownmusymmetric(
data=feldsparsangles, muknown=pi/3, M = 3, iter =1000, gradientstop=1e-10)
resfeldsparknownanglesymmetric
hist(feldsparsangles,breaks=seq(0,pi,pi/7),xlab="Orientations (radians)",freq=FALSE,
ylab="",main="",ylim=c(0,.8),axes=FALSE)
axialnntsplot(resfeldsparknownanglesymmetric$cestimatesmuunknown[,2],3,add=TRUE)
axialnntsplot(resfeldsparknownanglesymmetric$cestimatesmuknown[,2],3,add=TRUE,lty=2)
axis(1,at=c(0,pi/2,pi),labels=c("0",expression(pi/2),expression(pi)),las=1)
axis(2)

CircNNTSRaxial documentation built on June 8, 2025, 10:51 a.m.