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

Shota Katayama, Hironori Fujisawa

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1243-1264
ページ数22
ジャーナルStatistica Sinica
27
3
DOI
出版ステータスPublished - 2017 7月
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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