The Bag-and-Whisker Plot: A New Bagplot for Bivariate Data

TL;DR

This paper introduces a new bag-and-whisker plot for bivariate data that improves outlier detection adaptivity and visualization stability, making it more reliable and practical for real-world applications.

Contribution

The paper proposes a data-adaptive fence based on multiple testing and a refined visualization that replaces the convex hull, enhancing robustness and interpretability of the bagplot.

Findings

Superior adaptivity in outlier detection

Enhanced robustness and stability

Effective visualization of data spread

Abstract

The bagplot, also known as the "bag-and-bolster plot", is a notable extension of the boxplot from univariate to bivariate data. Although widely used, its practical application is hindered by two key limitations: the fixed inflation factor for outlier detection that does not adapt to the sample size, and the unstable convex hull used to visualize its fence. In this paper, we propose a new bagplot, namely the "bag-and-whisker plot'', as an improvement method to address these limitations. Our framework recasts outlier detection as a multiple testing problem, yielding a data-adaptive fence that controls statistical error rates and enhances the reliability of outlier identification. To further resolve graphical instability, we introduce a refined visualization that abandons the convex hull (the bolster) with a direct rendering of the statistical fence, complemented by granular whiskers that effectively illustrate the data's spread. Extensive simulations and real-world data analyses demonstrate that our new bagplot exhibits superior adaptivity and robustness compared to the existing standard, and thus can be highly recommended for practical use.