A statistician may face with a dataset that suffers from multicollinearity and outliers, simultaneously. The Huberized ridge (HR) estimator is a technique that can be used here. On the other hand, an expert may claim that some/all the variables should be removed from the analysis, due to inappropriateness, that imposes a prior information that all coefficients equal to zero (in the form of a restriction) to the analysis. In such situations, one may consider the HR estimation under the subspace restriction. In this paper, we introduce some improved estimators for verifying this claim. They are employed to improve the performance of the HR estimator in the multiple regression model. Advantages of the proposed estimators over the usual HR estimator are demonstrated through a Monte Carlo simulation as well as two real data examples.

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