In this paper we introduce a class of estimators which includes the ordinary least squares (OLS), the principal components regression (PCR) and the Liu estimator (1). In particular, we show that our new estimator is superior, in the scalar meansquared error (mse) sense, to the Liu estimator, to the OLS estimator and to the PCR estimator.
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.
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