  The telegraph process $\{X(t), t>0\}$, is supposed to be observed at $n+1$
equidistant time points $t_i=i\Delta_n,i=0,1,..., n$. The unknown value of
$\lambda$, the underlying rate of the Poisson process, is a parameter to be
estimated. The asymptotic framework considered is the following:
  $\Delta_n \to 0$, $n\Delta_n = T \to \infty$ as $n \to \infty$. We show that
previously proposed moment type estimators are consistent and asymptotically
normal but not efficient. We study further an approximated moment type
estimator which is still not efficient but comes in explicit form. For this
estimator the additional assumption $n\Delta_n^3 \to 0$ is required in order to
obtain asymptotic normality. Finally, we propose a new estimator which is
consistent, asymptotically normal and asymptotically efficient under no
additional hypotheses.
