Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 79; no. 1; pp. 247 - 265
• Main Authors: Fan, Jianqing, Li, Quefeng, Wang, Yuyan
• Format: Journal Article
• Language: English
• Published: England John Wiley & Sons Ltd 01.01.2017; Oxford University Press
• Subjects: algorithms; Analysis; Byproducts; Deviation; equations; Errors; Estimators; heteroskedasticity; High dimension; Huber loss; Mathematical analysis; Mathematical models; M‐estimator; Optimal rate; Quantiles; Regression; Regression analysis; Robust regularization; Statistical methods; Statistics; Studies; High dimension; Robust regularization; Huber loss; M-estimator; Optimal rate

Data subject to heavy-tailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and least absolute deviation regression have been developed in recent years. These methods essentially estimate the conditional median (or quant...