We have then cov p1 pq i 22 b 3045 actuarial

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Unformatted text preview: = (β1 , · · · , βp+q ). The test statistic of the Wald test has a χ2 distribution with q degrees of freedom under the null hypothesis for large n. In general, the Likelihood ratio test and the Wald test give very similar conclusions in practice. (Note: Here, the vectors are row vectors. In statistics literature, column vectors seem more popular.) 29/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Hypothesis tests on the β ’s Covariance term Recall the observed information matrix of the model with p + q covariates is I (b ) = − ∂ 2 ln Lp+q (β ) |β =b ∂βi ∂βj i ,j =1,··· ,p +q Now partition (I (b ))−1 into (I (b ))−1 = I (11) (b ) I (12) (b ) I (21) (b ) I (22) (b ) where I11 (b ) is of dimension p × p , and I (22) (b ) is of dimension q × q . We have then ˜ ˜ Cov (βp+1 , · · · , βp+q ) = I (22) (b ) 30/45 Actuarial Statistics – Module 3: Semi-parametric methods: Cox Regression Model Hypothesis tests on the β ’...
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This document was uploaded on 04/03/2014.

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