Minimum-variance unbiased estimator

Multicollinearity

Mathematics

Invariant estimator

Statistics

Stein's unbiased risk estimate

Mean squared error

James–Stein estimator

Estimator

Bias of an estimator

Consistent estimator

Trimmed estimator

Linear regression

Applied mathematics

Efficient estimator

Ordinary least squares

Modelling and Simulation in Engineering

The literature has shown that ordinary least squares estimator (OLSE) is not best when the explanatory variables are related, that is, when multicollinearity is present. This estimator becomes unstable and gives a misleading conclusion. In this study, a modified new two-parameter estimator based on prior information for the vector of parameters is proposed to circumvent the problem of multicollinearity. This new estimator includes the special cases of the ordinary least squares estimator (OLSE), the ridge estimator (RRE), the Liu estimator (LE), the modified ridge estimator (MRE), and the modified Liu estimator (MLE). Furthermore, the superiority of the new estimator over OLSE, RRE, LE, MRE, MLE, and the two-parameter estimator proposed by Ozkale and Kaciranlar (2007) was obtained by using the mean squared error matrix criterion. In conclusion, a numerical example and a simulation study were conducted to illustrate the theoretical results.

A Modified New Two-Parameter Estimator in a Linear Regression Model