CircNNTSR (version 2.0)

mnntsmanifoldnewtonestimation: Parameter estimation for MNNTS distributions

Description

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

Usage

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

Arguments

data

a 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

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. First M[1]+1 elements correspond to dimension 1, next M[2]+1 elements c

Value

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

Examples

M<-c(2,3)
R<-length(M)
data(Nest)
data<-Nest
est<-mnntsmanifoldnewtonestimation(data,M,R,1000)
est