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

ABSTRACT: 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 (LAD) regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression functions in ultra-high dimensional setting with existence of only the second moment? To solve this problem, we propose a penalized Huber loss with diverging parameter to reduce biases created by the traditional Huber loss. Such a penalized robust approximate quadratic (RA-quadratic) loss will be

SUBMITTER: Fan J 

PROVIDER: S-EPMC5412601 | biostudies-literature | 2017 Jan

REPOSITORIES: biostudies-literature