A multiple-case deletion approach for detecting influential points in high-dimensional regression

ABSTRACT

In high-dimensional regression, the presence of influential observations may lead to inaccurate analysis results so that it is a prime and important issue to detect these unusual points before statistical regression analysis. Most of the traditional approaches are, however, based on single-case diagnostics, and they may fail due to the presence of multiple influential observations that suffer from masking effects. In this paper, an adaptive multiple-case deletion approach is proposed for detecting multiple influential observations in the presence of masking effects in high-dimensional regression. The procedure contains two stages. Firstly, we propose a multiple-case deletion technique, and obtain an approximate clean subset of the data that is presumably free of influential observations. To enhance efficiency, in the second stage, we refine the detection rule. Monte Carlo simulation studies and a real-life data analysis investigate the effective performance of the proposed procedure.

KEYWORDS:

• High-dimensional regression
• Influential points
• Masking
• Regression diagnostics

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J20
• 62H15
• 62J05

Acknowledgements

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

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China (grants 11571191, 11431006 and 11401245), and Project Funded by the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.