Robust estimation and shrinkage in ultrahigh dimensional expectile regression with heavy tails and variance heterogeneity

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square loss and huber-type robust technique to develop the robust ex...

Full description

Saved in:
Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2022-02, Vol.63 (1), p.1-28
Main Authors: Zhao, Jun, Yan, Guan’ao, Zhang, Yi
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Asymmetry
Bias
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Heterogeneity
Insurance
Management
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Penalty function
Probability Theory and Stochastic Processes
Regular Article
Robustness (mathematics)
Statistical analysis
Statistical methods
Statistics
Statistics for Business
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square loss and huber-type robust technique to develop the robust expectile regression for ultrahigh dimensional heavy-tailed heterogeneous data. Different from the classical huber method, we introduce two different tuning parameters on both sides to account for possibly asymmetry and allow them to diverge to reduce bias induced by the robust approximation. In the regularized framework, we adopt the generally folded concave penalty function like the SCAD or MCP penalty for the seek of bias reduction. We investigate the finite sample property of the corresponding estimator and figure out how our method plays its role to trade off the estimation accuracy against the heavy-tailed distribution. Also, based on our theoretical study, we propose an efficient first-order optimization algorithm after locally linear approximation of the non-convex problem. Simulation studies under various distributions and a real data example demonstrate the satisfactory performances of our method in coefficient estimation, model selection and heterogeneity detection.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-021-01227-2