The Constrained Maximum Likelihood Estimation For Parameters Arising   From Partially Identified Models
  We extend the constrained maximum likelihood estimation theory for parameters of a completely identified model, proposed by Aitchison and Silvey (1958), to parameters arising from a partially identified model. With a partially identified model, some parameters of the model may only be identified through constraints imposed by additional assumptions. We show that, under certain conditions, the constrained maximum likelihood estimator exists and locally maximize the likelihood function subject to constraints. We then study the asymptotic distribution of the estimator and propose a numerical algorithm for estimating parameters. We also discuss a special situation where exploiting additional assumptions does not improve estimation efficiency. 
Hao Luo, Alexandre Bouchard-C\^ot\'e, Gabriela Cohen Freue, Paul   Gustafson
math.ST stat.TH