The Bag-and-Whisker Plot: A New Bagplot for Bivariate Data
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911306059087872 |
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| author | Qin, Shenghao Gang, Bowen Tong, Tiejun Cui, Hengjian |
| author_facet | Qin, Shenghao Gang, Bowen Tong, Tiejun Cui, Hengjian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Bag-and-Whisker Plot: A New Bagplot for Bivariate Data Qin, Shenghao Gang, Bowen Tong, Tiejun Cui, Hengjian Methodology 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. |
| title | The Bag-and-Whisker Plot: A New Bagplot for Bivariate Data |
| topic | Methodology |
| url | https://arxiv.org/abs/2512.06314 |