the current paper can be easily combined with those variable selection approaches. In particular, we will incorporate a modified version of the Adaptive LASSO into our procedure and verify its oracle property.

The rest of this paper is organized as follows. In Section 2, we will sketch the estimation procedures in detail. The large sample properties of resulting estimators are stated in Section 3. Simulation results and the application to real world data are presented in Section 4. Section 5 discusses some extensions of our model and concludes. All proofs are collected in Appendix.

ESTIMATION PROCEDURE
====================

The estimation procedure is based on maximizing the full information likelihood function which is formed as the product of joint pdf of the failure time $T\in[t,t+dt)$ and the observation of the longitudinal measure $Z_{t}$ at time $t$. To deal with the non-parametric $\lambda_{0}$, we adopt the method that approximates $\lambda_{0}$ through a sequence of finite dimensional step-wise functions, denoted as $\lambda_{n}^{s}$, with the number of steps given by the sample size $n$.

Throughout this section, we assume the data input for the estimation procedure only has the observation at the time to event, such as $\left\{\left(Z_{T_i},T_i\right):\,i=1,\dots,n\right\}$, while in the remark section, we will 