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Adaptive Huber Regression.

Qiang Sun1, Wen-Xin Zhou2, Jianqing Fan3

  • 1Department of Statistical Sciences, University of Toronto, Toronto, ON M5S 3G3, Canada.

Journal of the American Statistical Association
|November 3, 2020
PubMed
Summary
This summary is machine-generated.

Adaptive Huber regression offers robust estimation for big data with outliers and heavy tails. This new method provides optimal bias-robustness trade-offs, outperforming conventional techniques in statistical analysis and genetic studies.

Keywords:
Adaptive Huber regressionbias and robustness tradeofffinite-sample inferenceheavy-tailed datanonasymptotic optimalityphase transition

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • Big data often contains outliers and heavy-tailed distributions, challenging conventional statistical methods.
  • Robust estimation techniques are crucial for reliable analysis in such scenarios.

Purpose of the Study:

  • To propose adaptive Huber regression for robust estimation and inference in the presence of data contamination.
  • To develop a theoretical framework for heavy-tailed distributions and establish phase transitions for robust estimation.

Main Methods:

  • Adaptive Huber regression with a robustification parameter adapting to sample size, dimension, and moments.
  • Theoretical analysis for heavy-tailed distributions with bounded (1+δ)-th moments.
  • Extension to handle heavy-tailed predictors and observation noise.

Main Results:

  • Established sharp phase transitions for robust estimation in low and high dimensions.
  • Demonstrated sub-Gaussian-type deviation bounds for δ ≥ 1 without sub-Gaussian assumptions.
  • Identified optimal rates for 0 < δ < 1 and smooth transitions.

Conclusions:

  • Adaptive Huber regression provides a robust and predictive solution for big data challenges.
  • The method shows superior performance in simulations and a real-world genetic study of cancer cell lines.