Partial projective resampling method for dimension reduction: With applications to partially linear models

In many regression applications, the predictors naturally fall into two categories: “the predictors of primary interest” and “the predictors of secondary interest”. It is often desirable to have a dimension reduction method that focuses on the predictors of primary interest while controlling the effect of the predictors of secondary interest. To achieve this goal, a partial dimension reduction method via projective resampling of a composite vector containing the response variable(s) and the predictors of secondary interest is proposed. The proposed method is general in the sense that the predictors of secondary interest can be quantitative, categorical or a combination of both. An application of the proposed method for estimation in partially linear models is emphasized. The performance of the proposed method is assessed and compared with other competing methods via extensive simulation. The empirical results show that, in addition to the superior estimation accuracy, the proposed method has a considerable computational advantage. We also demonstrate the usefulness of the proposed method by analyzing two real datasets.