Ridge Estimation under the Stochastic Restriction

In linear programming and modeling of an economic system, there may occur some linear stochastic artificial or unnatural manners, which may need serious attentions. These stochastic unusual uncertainty, say stochastic constraints, definitely cause some changes in the estimators under work and their behaviors. In this approach, we are basically concerned with the problem of multicollinearity, when it is suspected that the parameter space may be restricted to some stochastic restrictions. We develop the estimation strategy form unbiasedness to some improved biased adjustment. In this regard, we study the performance of shrinkage estimators under the assumption of elliptically contoured errors and derive the region of optimality of each one. Lastly, a numerical example is taken to determine the adequate ridge parameter for each given estimator.