|
Abstract:
|
We derive the full likelihood function for regression parameter $\beta_0$ and baseline distribution function $F_0$ in the continuous Cox model. Using the empirical likelihood parameterization, we explicitly profile out nuisance parameter $F_0$ to obtain the full-profile likelihood function and the maximum likelihood estimator (MLE) for $\beta_0$. We show that the log full-likelihood ratio has an asymptotic chi-squared distribution, while the simulation studies indicate that for small or moderate sample sizes, the MLE performs favorably over Cox's partial likelihood estimator. Moreover, we show that the estimation bias of the MLE is asymptotically smaller than that of Cox's partial likelihood estimator. In a real data set example, our full likelihood ratio test and Cox's partial likelihood ratio test lead to statistically different conclusions. Part of this work is joint with Mai Zhou.
|
