13_AS_3_lec_a

# p we will select the ones that maximize the partial

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 12/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Estimation of the regression parameters β Partial likelihood estimation of β To estimate β = (β1 , β2 , . . . βp ), we will select the ones that maximize the partial likelihood under the following assumptions: noninformative censoring lives are independent Notation: Ordered times of observed death are t1 < t2 < · · · < tk dj : number of deaths occuring at time tj (1 ≤ j ≤ k ) We will label all the lives as 1, · · · , n. R (tj ) is the set of the label of all lives who are still under study at a time just prior to tj . Use (j ) to denote the label of the life who dies at tj 13/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Estimation of the regression parameters β Two cases We will distinguish two cases: 1 assume that only one death occurs at each tj (dj = 1 for 1 ≤ j ≤ k ) 2 Relax that assumption. In practice there might be ties in the data, that is 1 2 some dj > 1; or s...
View Full Document

## This document was uploaded on 04/03/2014.

Ask a homework question - tutors are online