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《高维普通最小二乘投影变量筛选》的引理修正说明AI 解读

The conclusion in Lemma 5 in the supplementary material (SM) of Wang and Leng (2016), on which Theorems 1–3 rely, is incorrect. Here we provide an additional condition under which the conclusion of this lemma holds. We assume that the rows of the matrix X follow a Gaussian distribution with precision matrix Ω = Σ−1 that satisfies c 4 - 1 n - τ / 2 ≤ λ min ( Ω ) ≤ λ max ( Ω ) ≤ c 4 n τ / 2 . This implies the assumption on the condition number of Σ in Assumption A3. We drop…

用于变量筛选的高维普通最小二乘投影AI 解读

Summary 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…