mnntsmanifoldnewtonestimation {CircNNTSR}

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 \left(\frac{1}{2*pi}\right)^R.

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

Fernandez-Duran, J.J., Gregorio-Dominguez, M.M. (2014). Modeling Angles in Proteins and Circular Genomes Using Multivariate Angular Distributions Based on Nonnegative Trigonometric Sums. Statistical Applications in Genetics and Molecular Biology, 13(1), 1-18. doi:10.1515/sagmb-2012-0012

Examples

	set.seed(200)
M<-c(2,3)
R<-length(M)
data(Nest)
data<-Nest*(pi/180)
est<-mnntsmanifoldnewtonestimation(data,M,R,100)
est