The bagplot: A bivariate boxplot

We propose the bagplot, a bivariate generalization of the univariate boxplo t. The key notion is the halfspace location depth of a point relative to a bivariate dataset, which extends the univariate concept of rank. The "depth median" is the deepest location, and it is surrounded by a "bag" containin g the n/2 observations with largest depth. Magnifying the bag by a factor 3 yields the "fence" (which is not plotted). Observations between the bag an d the fence are marked by a light gray loop, whereas observations outside t he fence are flagged as outliers. The bagplot visualizes the location, spre ad, correlation, skewness, and tails of the data. It is equivariant for lin ear transformations, and not limited to elliptical distributions. Software for drawing the bagplot is made available for the S-Plus and MATLAB environ ments. The bagplot is illustrated on several datasets-for example, in a sca tterplot matrix of multivariate data.