  We consider the problem of parameter estimation by observations of
inhomogeneous Poisson process. It is well-known that if the regularity
conditions are fulfilled then the maximum likelihood and Bayesian estimators
are consistent, asymptotically normal and asymptotically efficient. These
regularity conditions can be roughly presented as follows: a) the intensity
function of observed process belongs to known parametric family of functions,
b) the model is identifiable, c) the Fisher information is positive continuous
function, d) the intensity function is sufficiently smooth with respect to the
unknown parameter, e) this parameter is an interior point of the interval. We
are interested in the properties of estimators when these regularity conditions
are not fulfilled. More precisely, we preset a review of the results which
correspond to the rejection of these conditions one by one and we show how the
properties of the MLE and Bayesian estimators change. The proofs of these
results are essentially based on some general results by Ibragimov and
Khasminskii.
