CIRJE-J-18. Kubokawa, Tatsuya, "Random Effects and Restriction of Parameters: A Review" October 1999.

Random effects and restriction of parameters are important concepts in constructing statistical models based on small samples: Restricting the parameter spaces to subspaces constrained by inequalities or equalities yields pooling the data to get stablized estimators, and incorporating the random effects into the models produces shrinkage procedures more accurate than usual crude estimators. This paper gives a review on the random effects and the restriction of parameters and demonstrates the importance of these two concepts in an example of small area estimation. It is also explained that the shrinkage estimators have interesting relation with the factor analysis, the Kalman filter and the Spline smoothing method.