snntsmanifoldnewtonestimation {CircNNTSR} R Documentation

## Parameter estimation for SNNTS distributions for spherical data

### Description

Computes the maximum likelihood estimates of the SNNTS model parameters using a Newton algorithm on the hypersphere

### Usage

```snntsmanifoldnewtonestimation(data, M = c(0,0), iter = 1000,
initialpoint = FALSE, cinitial)```

### Arguments

 `data` Matrix of angles in radians, with one row for each data point. The first column contains longitude data (between zero and 2*pi), and second column contains latitude data (between zero and pi), with one row for each data point `M` Vector with number of components in the SNNTS for each dimension `iter` Number of iterations `initialpoint` TRUE if an initial point for the optimization algorithm will be used `cinitial` Initial value for cpars for the optimization algorithm, avector of complex numbers of dimension prod(M+1). The first element is a real and positive number. The sum of the squared moduli of the c parameters must be equal to one.

### Value

 `cestimates` Matrix of prod(M+1)*(3). The first two columns are the parameter numbers, and the last 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

### Note

The parameters cinitial and cestimates used by this function are the transformed parameters of the SNNTS density function, which lie on the surface of the unit hypersphere

### Author(s)

Juan Jose Fernandez-Duran and Maria Mercedes Gregorio-Dominguez

### References

Fernandez-Duran J. J. y Gregorio Dominguez, M. M. (2008) Spherical Distributions Based on Nonnegative Trigonometric Sums, Working Paper, Statistics Department, ITAM, DE-C08.6

### Examples

```set.seed(200)

M<-c(4,4)
cpar<-rnorm(prod(M+1))+rnorm(prod(M+1))*complex(real=0,imaginary=1)
cpar[1]<-Re(cpar[1])
cpar<- cpar/sqrt(sum(Mod(cpar)^2))

cest<-snntsmanifoldnewtonestimation(data,c(4,4),100,TRUE,cpar)
cest
cest<-snntsmanifoldnewtonestimation(data,c(1,2),100)
cest

```

[Package CircNNTSR version 2.2-1 Index]