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Blockwise missing data present a great challenge for data analysis because of their special missing structure. In this article, we propose a novel weighted multiple blockwise imputation method to target the problem of high-dimensional regression with blockwise missing data. Specifically, we first apply a multiple blockwise imputation technique to impute the missing blocks in the design matrix, after which a weighted sum formula is used to integrate the resulting imputation schemes and estimate the regression coefficients. The proposed method can make full use of the available information to perform imputation; hence, it shows superior performance compared to some previous methods. Simulations illustrate the advantageous numerical performance of our method in terms of variable selection, parameter estimation, and prediction ability. A real application is also presented to demonstrate its practical merit.

Weighted multiple blockwise imputation method for high-dimensional regression with blockwise missing data