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Why in Cox's regression model partial likelihood is used instead of ordinary likelihood function?
Wiki User
∙ 13y ago
Cox model applies to observations in time (i.e. processes, or functions of t). The true likelihood for that function would be a function of (functions of t), obtained by expressing the probability in a space of (functions of t) as
[density]*[reference measure on (functions of t)]
The factor [density] would be the true likelihood.
The partial likelihood is a factor of [density] involving only the parameters of interest:
[density] = [partial likelihood]*[....]
There is no point in working with the full likelihood, in the sense that the nice properties of the MLE apply to parameters from a finite dimensional space, and would not automatically apply to the full likelihood in the space of (functiosn of t).
That is why, for example, one needs to rework the large sample theory of estimators based on partial likelihood.
Wiki User
∙ 13y ago
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