Abstract:
Instead of using the Ordinary Least Square Estimator (OLSE) to estimate the regression
coefficients, the biased estimators are proposed in the multiple linear regression to overcome the
multicollinearity among the predictor variables. An alternative technique to solve the
multicollinearity problem is to consider parameter estimation with some restrictions on the
unknown parameters, which may be exact or stochastic restrictions. In this research, we propose a
biased estimator, namely new stochastic restricted two parameter estimator (NSRTPE) in a multiple
linear regression model to tackle the multicollinearity problem when the stochastic restrictions are
available. The proposed estimator over the ordinary least square estimator (OLSE), ridge estimator
(RE), Liu estimator (LE), almost unbiased Liu estimator (AULE), modified new two parameter
estimator (MNTPE), mixed estimator (ME), stochastic restricted Liu estimator (SRLE) are
compared in the scalar mean square error (SMSE) sense through a simulation study by considering
different levels of multicollinearity and different values of shrinkage parameters (k and d) selected
within the interval 0 to 1. From the simulation study, it can be noticed that the proposed estimator
performs well than existing estimators when the value of d is large. Furthermore, it can be observed
that the proposed estimator is always superior to MNTPE. Finally, it could be concluded that the
proposed estimator is meaningful in practice.
Keywords: Multiple linear regression; Multicollinearity; Stochastic restriction; New stochastic
restricted two parameter estimator; Scalar Mean square error
