Estimation under Multicollinearity : Application of Restricted Liu and Maximum Entropy Estimators to the Portland Cement Dataset

2. Various Methods of Estimation under Severe Multicollinearity Conditions: In what follows, we give a brief account of some important methods of estimation under severe multicollinearity conditions: (i). The Restricted Least Squares (RLS) Estimator of β : If we can put some restriction on the linear combination of regression coefficients such that , R r β = then the RLS estimator of β denoted by * β is given by * 1 1 1 1 ˆ ˆ ˆ ( ) ( ) : ; S R RS R r R S X y S X X β β β β − − − − ′ ′ ′ ′ = + − = = . (ii). The Ordinary Ridge Regression (ORR) Estimator of β : As suggested by Hoerl and Kennard (1970) it is possible to mitigate the multicollinearity problem by perturbation of S matrix such that its principal diagonal elements are inflated. The Ordinary Ridge Regression estimator is given by 1 ˆ ( ) ( ) S I X y β κ κ − ′ = + . As stated by Kaçiranlar et al., writing 1 1 ( ) W I S κ κ − − = + we may