Outlier detection using difference-based variance estimators in multiple regression

ABSTRACT

In this article, we propose an outlier detection approach in a multiple regression model using the properties of a difference-based variance estimator. This type of a difference-based variance estimator was originally used to estimate error variance in a non parametric regression model without estimating a non parametric function. This article first employed a difference-based error variance estimator to study the outlier detection problem in a multiple regression model. Our approach uses the leave-one-out type method based on difference-based error variance. The existing outlier detection approaches using the leave-one-out approach are highly affected by other outliers, while ours is not because our approach does not use the regression coefficient estimator. We compared our approach with several existing methods using a simulation study, suggesting the outperformance of our approach. The advantages of our approach are demonstrated using a real data application. Our approach can be extended to the non parametric regression model for outlier detection.

KEYWORDS:

• Difference-based error variance estimator
• Least squares
• Leave-one-out approach.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J20
• 62J05

Additional information

Funding

This study was supported in part by the National Science Foundation grant (NSF-CNS 096480) and National Science Foundation grant (NSF-CNS 1115839).