NBtsVarSel (version 1.0)

grad_hess_beta: Gradient and Hessian of the log-likelihood with respect to beta

Description

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

Usage

grad_hess_beta(Y, X, beta, gamma, alpha)

Value

grad_L_beta

Vector of the gradient of L with respect to beta

hess_L_beta

Matrix of the Hessian of L with respect to beta

Arguments

Y

Observation matrix

X

Design matrix

beta

Initial beta vector

gamma

Initial gamma vector

alpha

Initial overdispertion parameter

Author

Marina Gomtsyan

Maintainer: Marina Gomtsyan <[e-mail]>

References

M. Gomtsyan "Variable selection in a specific regression time series of counts.", arXiv:2307.00929

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_nb = glm.nb(Y~t(X)[,2:(p+1)])
beta0 = as.numeric(glm_nb$coefficients)
alpha0 = glm_nb$theta
result = grad_hess_beta(Y, X, beta0, gamma0, alpha0)
grad = result$grad_L_beta
Hessian = result$hess_L_beta