Martingales on Jump Processes. II: Applications

summary:The longitudinal regression model $Z_i^j=m(\theta _0,{\mathbb{X}}_i(T_i^j))+ \varepsilon _i^j,$ where $Z_i^j$ is the $j$th measurement of the $i$th subject at random time $T_i^j$, $m$ is the regression function, ${\mathbb{X}}_i(T_i^j)$ is a predictable covariate process observed at time $T_i^j$ and $\varepsilon _i^j$ is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth $M$-estimator of unknown parameter $\theta _0$