In a non–life insurance business an insurer often needs to build up a reserve to able to meet his or her future obligations arising from incurred but not reported completely claims. To forecast these claims reserves, a simple but generally accepted algorithm is the classical chain-ladder method. Recent research essentially focused on the underlying model for the claims reserves to come to appropriate bounds for the estimates of future claims reserves. Our research concentrates on scenarios with outlying data. On closer examination it is demonstrated that the forecasts for future claims reserves are very dependent on outlying observations. The paper focuses on two approaches to robustify the chain-ladder method: the first method detects and adjusts the outlying values, whereas the second method is based on a robust generalized linear model technique. In this way insurers will be able to find a reserve that is similar to the reserve they would have found if the data contained no outliers. Because the robust method flags the outliers, it is possible to examine these observations for further examination. For obtaining the corresponding standard errors the bootstrapping technique is applied. The robust chain-ladder method is applied to several run-off triangles with and without outliers, showing its excellent performance.

Most outlier detection rules for multivariate data are based on the assumption of elliptical symmetry of the underlying distribution. We propose an outlier detection method which does not need the assumption of symmetry and does not rely on visual inspection. Our method is a generalization of the Stahel-Donoho outlyingness. The latter approach assigns to each observation a measure of outlyingness, which is obtained by projection pursuit techniques that only use univariate robust measures of location and scale. To allow skewness in the data, we adjust this measure of outlyingness by using a robust measure of skewness as well. The observations corresponding to an outlying value of the adjusted outlyingness are then considered as outliers. For bivariate data, our approach leads to two graphical representations. The first one is a contour plot of the adjusted outlyingness values, and can be considered as an approximation of the density contours of the underlying distribution. We also construct an extension of the boxplot for bivariate data, in the spirit of the bagplot [1] which is based on the concept of half space depth. We illustrate our outlier detection method on several simulated and real data.

Abstract—Node-link diagrams are an effective and popular visualization approach for depicting hierarchical structures and for showing parent-child relationships. In this paper, we present the results of an eye tracking experiment investigating traditional, orthogonal, and radial node-link tree layouts as a piece of empirical basis for choosing between those layouts. Eye tracking was used to identify visual exploration behaviors of participants that were asked to solve a typical hierarchy exploration task by inspecting a static tree diagram: finding the least common ancestor of a given set of marked leaf nodes. To uncover exploration strategies, we examined fixation points, duration, and saccades of participants ’ gaze trajectories. For the non-radial diagrams, we additionally investigated the effect of diagram orientation by switching the position of the root node to each of the four main orientations. We also recorded and analyzed correctness of answers as well as completion times in addition to the eye movement data. We found out that traditional and orthogonal tree layouts significantly outperform radial tree layouts for the given task. Furthermore, by applying trajectory analysis techniques we uncovered that participants cross-checked their task solution more often in the radial than in the non-radial layouts. Index Terms—Hierarchy visualization, node-link layout, eye tracking, user study. 1