More on the restricted ridge regression estimation

Abstract

Several alternative methods for derivation of the restricted ridge regression estimator (RRRE) are provided. Theoretical comparison and relationship of RRRE with related methods for regression with the multicollinearity problem are described. We also find inter-connections among RRRE, ordinary ridge regression estimator (ORRE), restricted least squares estimator (RLSE), modified ridge regression estimator (MRRE) and restricted modified generalized ridge estimator (RMGRE). Finally, numerical comparison, in addition to theoretical derivation, is also conducted with a Monte Carlo simulation and a real data example.

AMS Subject Classification :

• 62J05
• 62J07
• 62P20

Keywords:

• mean square error
• multicollinearity
• restricted least squares
• ridge regression
• restricted ridge regression

Notes

Tables are not given in the paper for space saving considerations and are available upon request.

There are no changes in the explanatory variables for some observations. We excluded these observations, since they produce a zero denominator.

The first value of b, which is equal to 0.6, belongs to the intercept term. This value is chosen arbitrarily by investigation of mse values of MRRE. The prior information for β₂, β₃ and β₄ are chosen as 0, 0.6 and −0.5, respectively, since 0.5, 0.43 and −0.10 do not decrease the mse of MRRE to the desired levels.

This could be explained as the property that . Since MRRE approaches to a constant, its mse approaches to zero. Therefore, may yield misleading results and should be used with caution.