Rate of convergence in the maximum likelihood estimation for partial   discrete parameter, with applications to the cluster analysis and philology
  The problem of estimation of the distribution parameters on the sample when the part of these parameters are discrete (e.g. integer) is considered. We prove that the rate of convergence of MLE estimates under the natural conditions on the distribution density is exponentially fast. 
E.Ostrovsky, L.Sirota, A.Zeldin
math.ST stat.TH