This preview shows page 1. Sign up to view the full content.
Unformatted text preview: asterisk represent censored observations.
Using Breslow’s approximation, what contribution to the partial
likelihood is made by deaths at time 14?
20/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model
Estimation of the regression parameters β Solution Denote β = (β1 , β2 ).
Just prior to time 14, 4 lives are at risk and their covariates are
(0, 75), (1, 68), (1, 49) and (0, 86).
At time 14, there are two deaths with covariates (0, 75), (1, 68).
Hence, the contribution to the partial likelihood made by deaths at
time 14 is approximated by
exp β (0 + 1, 75 + 68)T
2 [exp (β (0, 75)T ) + exp (β (1, 68)T ) + exp (β (1, 49)T ) + exp (β (0, 86)T )] 21/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model
Estimation of the regression parameters β Properties of the maximum (partial) likelihood estimator
The eﬃcient score function is deﬁned by
u (β ) =
Solving u β ∂ ln L (β )
∂ ln L (β )
= 0 gives maximum likelihood estimate β ˜
The maximum partial likelihood estimator β (of β ) is
asymptotically (multivariate) normally distributed with mean
β and variance (matrix)...
View Full Document
This document was uploaded on 04/03/2014.
- Three '14