Another Look at High-Dimensional Regression in Principal Components Space and The Blessing of Dimensionality
主成分空间中的高维回归与维数增益：再考察
Benefits of exploiting sparsity in the space of principal components have been well documented both empirically and theoretically (Lang and Zou; Silin and Fan). In this article, we further reveal another unexpected advantage of exploiting sparsity in the space of principal components when the data are contaminated by measurement errors. Assuming the coefficient vector resides in an lq ball (0≤q≤1), we show that an l1 penalized principal components regression has a prediction…