Sparse and robust linear regression: An optimization algorithm and its statistical properties

Shota Katayama, Hironori Fujisawa

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and outliers is considered. The 1 penalty is imposed for the coefficients, while various penalties including redescending type penalties are for the outliers. To solve the sparse estimation problem, we introduce an optimization algorithm. Under some conditions, we show the algorithmic and statistical convergence property for the coefficients obtained by the algorithm. Moreover, it is shown that the algorithm can recover the true support of the coefficients with probability going to one.

Original languageEnglish
Pages (from-to)1243-1264
Number of pages22
JournalStatistica Sinica
Volume27
Issue number3
DOIs
Publication statusPublished - 2017 Jul
Externally publishedYes

Keywords

  • Algorithmic and statistical convergence
  • Robust estimation
  • Sparse linear regression
  • Support recovery

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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