CircNNTSR (version 2.3)

nntsmanifoldnewtonestimation: Parameter estimation for NNTS distributions

Description

Computes the maximum likelihood estimates of the NNTS parameters, using a Newton algorithm on the hypersphere

Usage

nntsmanifoldnewtonestimation(data, M=0, iter=1000, initialpoint = FALSE, cinitial)

Value

cestimates

Matrix of (M+1)x2. The first column is the parameter numbers, and the second column is the c parameter's estimators

loglik

Optimum log-likelihood value

AIC

Value of Akaike's Information Criterion

BIC

Value of Bayesian Information Criterion

gradnormerror

Gradient error after the last iteration

Arguments

data

Vector of angles in radians

M

Number of components in the NNTS

iter

Number of iterations

initialpoint

TRUE if an initial point for the optimization algorithm 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)

Author

Juan Jose Fernandez-Duran y Maria Mercedes Gregorio-Dominguez

References

Fernandez-Duran, J.J., Gregorio-Dominguez, M.M. (2010). Maximum Likelihood Estimation of Nonnegative Trigonometric Sums Models by Using a Newton-like Algorithm on Manifolds, Working Paper, Department of Statistics, ITAM, DE-C10.8

Examples

set.seed(200)
a<-c(runif(10,3*pi/2,2*pi-0.00000001),runif(10,pi/2,pi-0.00000001))
#Estimation of the NNTSdensity with 2 components for data and 200 iterations
nntsmanifoldnewtonestimation(a,2,iter=200)

data(Turtles_radians)
#Empirical analysis of data
Turtles_hist<-hist(Turtles_radians,breaks=10,freq=FALSE)
#Estimation of the NNTS density with 3 componentes for data
nntsmanifoldnewtonestimation(Turtles_radians,3,iter=200)