grad_hess_gamma {GlarmaVarSel}

Gradient and Hessian of the log-likelihood with respect to gamma

Description

This function calculates the gradient and Hessian of the log-likelihood with respect to gamma

Usage

grad_hess_gamma(Y, X, beta0, gamma0)

Arguments

Y

Observation matrix

X

Design matrix

beta0

Initial beta vector

gamma0

Initial gamma vector

Value

grad_L_gamma

Vector of the gradient of L with respect to gamma

hess_L_gamma

Matrix of the Hessian of L with respect to gamma

Author(s)

Marina Gomtsyan, Celine Levy-Leduc, Sarah Ouadah, Laure Sansonnet

Maintainer: Marina Gomtsyan <[e-mail]>

References

M. Gomtsyan et al. "Variable selection in sparse GLARMA models", arXiv:2007.08623v1

Examples

n=50
p=30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t]<-c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
glm_pois<-glm(Y~t(X)[,2:(p+1)],family = poisson)
beta0<-as.numeric(glm_pois$coefficients) 
result = grad_hess_gamma(Y, X, beta0, gamma0)
grad = result$grad_L_gamma
Hessian = result$hess_L_gamma