Multiple outliers detection in sparse high-dimensional regression

ABSTRACT

The presence of outliers would inevitably lead to distorted analysis and inappropriate prediction, especially for multiple outliers in high-dimensional regression, where the high dimensionality of the data might amplify the chance of an observation or multiple observations being outlying. Noting that the detection of outliers is not only necessary but also important in high-dimensional regression analysis, we, in this paper, propose a feasible outlier detection approach in sparse high-dimensional linear regression model. Firstly, we search a clean subset by use of the sure independence screening method and the least trimmed square regression estimates. Then, we define a high-dimensional outlier detection measure and propose a multiple outliers detection approach through multiple testing procedures. In addition, to enhance efficiency, we refine the outlier detection rule after obtaining a relatively reliable non-outlier subset based on the initial detection approach. By comparison studies based on Monte Carlo simulation, it is shown that the proposed method performs well for detecting multiple outliers in sparse high-dimensional linear regression model. We further illustrate the application of the proposed method by empirical analysis of a real-life protein and gene expression data.

KEYWORDS:

• High-dimensional linear regression
• least trimmed square
• multiple hypothesis testing
• multiple outliers detection

AMS SUBJECT CLASSIFICATION:

• 62J20
• 62H15
• 62J05
• 62F35

Acknowledgements

The authors are grateful to the editor, the associate editor and two anonymous referees for their comments that have greatly improved this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China [grants 11571191, 11371202, 11431006 and 11771187], and Project Funded by the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.