more attractive to the scenarios where there are only a few longitudinal observations but a large set of covariates.

Numerical Studies
=================

Simulation Studies {#simulation}
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In this section, simulation studies are conducted to evaluate the finite-sample performance of the estimation procedures proposed in section \[likelihood function\]. Consider the following examples:

\[example1\] 50 samples, each consisting of $n=400,\,800$ subjects, are generated from simulating the version of model that has covariate dimension $p=16$, coefficients $b_0=(1,1,-1,0,\dots,0)$ with $3$ non-zero covariate effects. Given $$a=(1,0.5,-1,0.3,1,0.5,-1,0.3,1,0.5,-1,0.3,1,0.5,
-1,0.3),$$ the conditional expectation function is specified as the constant function as below: $$\label{parametrized-conditional-growth-rate}
q\left(z,t\mid a\right)=a.$$ The baseline hazard is specified through the function $$\label{lambda0}
\lambda_0(t)=\frac{\exp(10)+\exp^{-t}}{\exp(10)+1}.$$ The initial $Z_0\sim N(0,I_{16})$ with $I_{16}$ being the $16$-dimensional identity matrix.

The simulation results are presented in the terms of the following criteria:

\(1) Figure \[fig: fitting\] shows the the estimated cumulative hazard $\int_{0}^{t}\hat{\lambda}_{n}^{s}(\tau)d\tau$ versus the true cumulative hazard \[lambda0\] for Example \[example1\]. The bias and standard deviation of the estimated non-zero $b_0$ are given in Table \[table: non-zero param\]. (2) We also conduct variable selection for both of the example \[example1\] by the adaptive LASSO method , the result are summarized in Table \[table: variable selection\] for Example \[example1\]. The result are 