mnntsmanifoldnewtonestimation {CircNNTSR} R Documentation

## Parameter estimation for the MNNTS distributions

### Description

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

### Usage

`mnntsmanifoldnewtonestimation(data,M=0,R=1,iter=1000,initialpoint=FALSE,cinitial)`

### Arguments

 `data` Matrix of angles in radians, a column for each dimension, a row for each data point `M` Vector of length R with number of components in the MNNTS for each dimension `R` Number of dimensions `iter` Number of iterations for the Newton algorithm `initialpoint` TRUE if an initial point for the optimization algorithm will be used `cinitial` Initial value for cpars (parameters of the model) for the optimization algorithm. Vector of complex numbers of dimension prod(M+1). The first element is a real and positive number. The first M[1]+1 elements correspond to dimension one, the next M[2]+1 elements correspond to dimension two, and so on. The sum of the SQUARED moduli of the c parameters must be equal to 1/(2*pi).

### Value

 `cestimates ` Matrix of prod(M+1)*(R+1). The first R columns are the parameter number, 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

### Author(s)

Juan Jose Fernandez-Duran and Maria Mercedes Gregorio-Dominguez

### References

Fernandez-Duran, J.J. and Gregorio-Dominguez, M.M. (2009) Multivariate Angular Distributions Based on Multiple Nonnegative Trigonometric Sums, Working Paper, Statistics Department, ITAM, DE-C09.1

### Examples

```	set.seed(200)
M<-c(2,3)
R<-length(M)
data(Nest)
data<-Nest
est<-mnntsmanifoldnewtonestimation(data,M,R,100)
est
```

[Package CircNNTSR version 2.2-1 Index]