p we will select the ones that maximize the partial

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

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