nntsmanifoldnewtonestimationsymmetryknownsymmetryanglemu {CircNNTSRSymmetric} | R Documentation |
Parameter estimation for NNTS symmetric distributions
Description
Computes the maximum likelihood estimates of the NNTS parameters of an NNTS symmetric distribution with known angle of symmetry mu, using a Newton algorithm on the hypersphere
Usage
nntsmanifoldnewtonestimationsymmetryknownsymmetryanglemu(data, mu, M = 0,
iter=1000,gradientstop=1e-10,initialpoint=FALSE,cinitial)
Arguments
data |
Vector of angles in radians |
mu |
Known angle of symmetry of the NNTS symmetric model |
M |
Number of components in the NNTS symmetric density |
iter |
Number of iterations |
gradientstop |
The minimum value of the norm of the gradient to stop the Newton algorithm on the hypersphere |
initialpoint |
TRUE if an initial point for the optimization algorithm for the general (asymmetric) 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/(2*pi). This is the vector of parameters for the general (asymmetric) NNTS density |
Value
cestimatessym |
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 model |
mu |
Known angle of symmetry of the NNTS symmetric model |
logliksym |
Optimum log-likelihood value for the NNTS symmetric model |
AICsym |
Value of Akaike's Information Criterion for the NNTS symmetric model |
BICsym |
Value of Bayesian Information Criterion for the NNTS symmetric model |
gradnormerrorsym |
Gradient error after the last iteration for the estimation of the parameters of the NNTS symmetric model |
cestimatesnonsym |
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 model |
logliknonsym |
Optimum log-likelihood value for the general (non-symmetric) NNTS model |
AICnonsym |
Value of Akaike's Information Criterion for the general (non-symmetric) NNTS model |
BICnonsym |
Value of Bayesian Information Criterion for the general (non-symmetric) NNTS model |
gradnormerrornonsym |
Gradient error after the last iteration for the estimation of the parameters of the general (non-symmetric) NNTS model |
loglikratioforsym |
Value of the likelihood ratio test statistic for symmetry |
loglikratioforsympvalue |
Value of the asymptotic chi squared p-value of the likelihood ratio test statistic for symmetry |
Author(s)
Juan Jose Fernandez-Duran y Maria Mercedes Gregorio-Dominguez
References
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(Ants_radians)
resantssymmknownmu<-nntsmanifoldnewtonestimationsymmetryknownsymmetryanglemu(data=Ants_radians,
mu=pi, M = 4, iter =1000,gradientstop=1e-10)
resantssymmknownmu
hist(Ants_radians,breaks=seq(0,2*pi,2*pi/13),xlab="Direction (radians)",freq=FALSE,
ylab="",main="",ylim=c(0,.8),axes=FALSE)
nntsplot(resantssymmknownmu$cestimatessym[,2],4,add=TRUE)
nntsplot(resantssymmknownmu$cestimatesnonsym[,2],4,add=TRUE,lty=2)
axis(1,at=c(0,pi/2,pi,6*(pi/4),2*pi),labels=c("0",expression(pi/2),expression(pi),
expression(3*pi/2),expression(2*pi)),las=1)
axis(2)