nntsmanifoldnewtonestimationgradientstop {CircNNTSR}

Maximum likelihood estimates of the NNTS parameters

Description

Computes the maximum likelihood estimates of the NNTS parameters, using a Newton algorithm on the hypersphere with the option to specify a minimum value of the norm of the gradient error to stop the algorithm

Usage

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

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,\ldots,c_M). The sum of the squared moduli of the parameters must be equal to \frac{1}/{2\pi}

gradientstop

The value of the norm of the gradient error of the Newton algorithm at which the algorithms stops

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

Author(s)

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 gradientstop at 1e-12
nntsmanifoldnewtonestimationgradientstop(a,2,gradientstop=1e-12)
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 and gradientstop at 1e-12
nntsmanifoldnewtonestimationgradientstop(Turtles_radians,3,gradientstop=1e-12)