Asymptotics for generalized linear segmented regression models with an unknown breakpoint

We consider asymptotic theory for the maximum likelihood estimator
in the generalized linear model with an unknown breakpoint. A proof
for the asymptotic normality is given. The methods are based on the
work of Huber (1967). The main problem is the
non--differentiability of the likelihood and the score function,
which requires non--standard methods. An example from epidemiology
is presented, where confidence intervals for the parameters are
calculated with the asymptotic results.