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High dimensional ordinary least squares projection for screening variables

Variable selection is a challenging issue in statistical applications when the number of predictors p far exceeds the number of observations n. In this ultrahigh dimensional setting, the sure independence screening procedure was introduced to reduce the dimensionality significantly by preserving the true model with overwhelming probability, before a refined second‐stage analysis. However, the aforementioned sure screening property strongly relies on the assumption that the important variables in the model have large marginal correlations with the response, which rarely holds in reality. To overcome this, we propose a novel and simple screening technique called high dimensional ordinary least squares projection which we refer to as ‘HOLP’. We show that HOLP has the sure screening property and gives consistent variable selection without the strong correlation assumption, and it has a low computational complexity. A ridge‐type HOLP procedure is also discussed. Simulation study shows that HOLP performs competitively compared with many other marginal correlation‐based methods. An application to a mammalian eye disease data set illustrates the attractiveness of HOLP.