Defining a two-parameter estimator: a mathematical programming evidence

Two-parameter (TP) estimators are more advantageous to their one-parameter competitors since they have two biasing parameters that serve different purposes in linear regression model. At least one of these biasing parameters intends to gain a remedial impact for multicollinearity. Within this respect, we define a new TP estimator to eliminate the disorder originated from multicollinearity. Also, we perform theoretical comparisons for new TP estimator according to mean square error criterion. By minimizing the mean square error, we derive optimal estimators for both of the biasing parameters of this new estimator. Moreover, we recommend a mathematical programming approach to determine two biasing parameters, simultaneously. In this approach, we minimize the mean square error and improve the length of the newly defined TP estimator. In application part, computations regarding the estimations of the biasing parameters and mean square errors, and the length of the estimated coefficients are examined.