Variable selection via thresholding
本文提出一种简单的阈值法，能在温和条件下一致地选出相关变量，并得到稀疏、一致且渐近正态的估计量，适用于回归分析中的变量选择问题。
Abstract Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero, covariates without relationships to the response often manifest small but nonzero regression coefficients. The ad hoc procedure of discarding variables whose coefficients are smaller than some threshold is often employed in practice. We formally analyze a version of such thresholding procedures and develop a simple thresholding method that consistently estimates the set of relevant variables under mild regularity assumptions. Using this thresholding procedure, we propose a sparse, ‐consistent and asymptotically normal estimator whose nonzero elements do not exhibit shrinkage. The performance and applicability of our approach are examined via numerical studies of simulated and real data.