The longitudinal regression model $Y_{i,j} = m(V_\tau_{i,j}^i) +
\varepsilon_{i,j}$ where $Y_{i,j}$, is the $j$th measurement of the
$i$th subject at random time $\tau_{i,j}$, $m$ is the regression
function, $V_\tau_{i, j}$ is a predictable covariate process observed at time
$\tau_{i,j}$ and $\varepsilon_{i,j}$ is noise, often provides an adequate
framework for modeling and comparing groups of data. The proposed longitudinal
regression model is based on marked point process theory, and allows a quite
general dependency structure among the observations.
¶ In this paper we find the asymptotic distribution of the cumulative
regression function (CRF), and present a nonparametric test to compare the
regression functions for two groups of longitudinal data. The proposed test,
denoted the CRF test, is based on the cumulative regression function (CRF) and
is the regression equivalent of the log-rank test in survival analysis. We show
as a special case that the CRF test is valid for groups of independent
identically distributed regression data. Apart from the CRF test, we also
consider a maximal deviation statistic that may be used when the CRF test is
inefficient.