We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positively associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of the marginal expected shortfall, which is shown to be asymptotically normal. The finite sample performance of the estimator is investigated in a small simulation study. The method is also applied to estimate the expected amount of rainfall at a weather station given that there is a once every 100 years rainfall at another weather station nearby.

Aiming to estimate extreme precipitation forecast quantiles, we propose a nonparametric regression model that features a constant extreme value index. Using local linear quantile regression and an extrapolation technique from extreme value theory, we develop an estimator for conditional quantiles corresponding to extreme high probability levels. We establish uniform consistency and asymptotic normality of the estimators. In a simulation study, we examine the performance of our estimator on finite samples in comparison with a method assuming linear quantiles. On a precipitation data set in the Netherlands, these estimators have greater predictive skill compared to the upper member of ensemble forecasts provided by a numerical weather prediction model.

Temporal bipartite networks that describe how users interact with tasks or items over time have recently become available. Such temporal information allows us to explore user behavior in-depth. We propose two metrics, the relative switch frequency and distraction in time to measure a user’s sequential-tasking level, i.e. to what extent a user interacts with a task consecutively without interacting with other tasks in between. We analyze the sequential-tasking level of users in two real-world networks, an user-project and an user-artist network that record users’ contribution to software projects and users’ playing of musics from diverse artists respectively. We find that users in the user-project network tend to be more sequential-tasking than those in the user-artist network, suggesting a major difference in user behavior when subject to work related and hobby-related tasks. Moreover, we investigate the relation (rank correlation) between the two sequential-tasking measures and another 10 nodal features. Users that interact less frequently or more regularly in time (low deviation in the time interval between two interactions) or with fewer items tend to be more sequential-tasking in the user-project network. No strong correlation has been found in the user-artist network, which limits our ability to identify sequential-tasking users from other user features.

We propose an estimator of the marginal expected shortfall by considering a log transformation of a variable which has an infinite expectation. We establish the asymptotic normality of our estimator under general assumptions. A simulation study suggests that the estimation procedure is robust with respect to the choice of tuning parameters. Our estimator has lower bias and mean squared error than the empirical estimator when the latter is applicable.We illustrate our method on a tsunami dataset.