Kybernetika

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 $\theta_0$.