  In the competing risks problem, an important role is played by the cumulative
incidence function (CIF), whose value at time $t$ is the probability of failure
by time $t$ from a particular type of failure in the presence of other risks.
In some cases there are reasons to believe that the CIFs due to various types
of failure are linearly ordered. El Barmi et al. [3] studied the estimation and
inference procedures under this ordering when there are only two causes of
failure. In this paper we extend the results to the case of $k$ CIFs, where
$k\ge3$. Although the analyses are more challenging, we show that most of the
results in the 2-sample case carry over to this $k$-sample case.
