A note on the asymptotic efficiency of the restricted estimation

This paper provides a unified framework for the analysis of the stochastic and deterministic constrained estimation. In a general framework it is show that stochastic restrictions method estimates can be asymptotically more e.cient than estimates ignoring prior information, and can achieve efficiency of the restricted estimate if prior information grows faster than the sample information in the asymptotics. As an example of the applicability of the previous result, the maximum likelihood stochastically restricted criterion is provided.