  We have established a sparse estimation method for the generalized
exponential marked Hawkes process by the penalized method to the ordinary
method (P-O) estimator. Furthermore, we evaluated the probability of correct
variable selection. In order to achieve this, we established a framework for a
likelihood analysis and the P-O estimation when there might be nuisance
parameters and the true value of the parameter could be realized at the
boundary of the parameter space. Numerical simulations are given for several
important examples.
