Asymptotic Behavior of Cox's Partial Likelihood and its Application to Variable Selection.

ABSTRACT: For theoretical properties of variable selection procedures for Cox's model, we study the asymptotic behavior of partial likelihood for the Cox model. We find that the partial likelihood does not behave like an ordinary likelihood, whose sample average typically tends to its expected value, a finite number, in probability. Under some mild conditions, we prove that the sample average of partial likelihood tends to infinity at the rate of the logarithm of the sample size, in probability. We apply the asymptotic results on the partial likelihood to study tuning parameter selection for penalized partial likelihood. We find that the penalized partial likelihood with the generalized cross-validation (GCV) tuning parameter proposed in Fan and Li (2002) enjoys the model selection consistency prope

SUBMITTER: Li R 

PROVIDER: S-EPMC6168090 | biostudies-literature | 2018 Oct

REPOSITORIES: biostudies-literature