grad_hess_gamma function

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

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

grad_hess_gamma(Y, X, beta0, gamma0)

Arguments

• Y: Observation matrix
• X: Design matrix
• beta0: Initial beta vector
• gamma0: Initial gamma vector

Returns

• 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

References

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

Author(s)

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

Maintainer: Marina Gomtsyan marina.gomtsyan@agroparistech.fr

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