nntsmanifoldnewtonestimation {CircNNTSR} R Documentation

## 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)`

### 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)

### 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 200 iterations
nntsmanifoldnewtonestimation(a,2,iter=200)