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

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.