snntsmanifoldnewtonestimation {CircNNTSR}

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)
data(Datab6fisher_ready)
data<-Datab6fisher_ready

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