CircNNTSR (version 2.0)

nntsmanifoldnewtonestimation: Parameter estimation for NNTS distributions

Description

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

Usage

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

Arguments

data

a 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

A 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)

Value

• cestimates
  A matrix of (M+1)x2, the first column are the parameter number and the second column the parameter's c estimators
• loglik
  Optimum loglikelihood value
• AIC
  Value of Akaike's Information Criterion
• BIC
  Value of Bayesian Information Criterion
• gradnormerror
  Gradient's error after last iteration

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

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 1000 iterations
nntsmanifoldnewtonestimation(a,2,1000)

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)