Gilmour's approach to mixed and stochastic restricted ridge predictions in linear mixed models

This article is concerned with the predictions in linear mixed models under stochastic linear restrictions. Mixed and stochastic restricted ridge predictors are introduced by using Gilmour's approach. We also investigate assumptions that the variance parameters are not known under stochastic linear restrictions and attain estimators of variance parameters. Superiorities the linear combinations of the predictors are done in the sense of mean square error matrix criterion. Finally, a hypothetical data set is considered to illustrate the findings.