ABSTRACT
Suppose that n units are observed. The ith unit is tested under the explanatory variable x(i)(·). The data are supposed to be right censored. Set Si = Sx(i) . Under the model (9.1)
Si(t;β, γ, σ) = G0
{(∫ t 0
. (9.2)
Set
G(u) = G0(eu), u ∈ R, g(u) = −G′(u), h(u) = g(u)/G(u),
θ = (βT , γT , σ)T , fi(t, θ) = ∫ t 0
The likelihood function is
L(θ) = n∏ i=1
{ 1 σ eβ
i (fi(Xi, θ)) −1×
h
( 1 σ ln(fi(Xi, θ))
)}δi G
( 1 σ ln(fi(Xi, θ))
) . (9.3)
Denote by θˆ the maximum likelihood estimator of the parameter θ.
