Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties
Shota Katayama and Hironori Fujisawa
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 $\ell_{1}$ 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.
Preprint
http://arxiv.org/abs/1505.05257
Print
http://www3.stat.sinica.edu.tw/statistica/J27N3/J27N315/J27N315.html
