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.

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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.

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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.

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The estimation of high quantiles for very low probabilities of exceedance pn much smaller than 1/n (with n the sample size) remains a major challenge. For this purpose, the log-Generalized Weibull (log-GW) tail limit was recently proposed as regularity condition as an alternative to the Generalized Pareto (GP) tail limit, in order to avoid potentially severe bias in applications of the latter. Continuing in this direction, a new estimator for the log-GW tail index and a related quantile estimator are introduced. Both are constructed using the Hill estimator as building block. Sufficient conditions for asymptotic normality are established. These results, together with the results of simulations and an application, indicate that the new estimator fulfils the potential of the log-GW tail limit as a widely applicable model for high quantile estimation, showing a substantial reduction in bias as well as improved precision when compared to an estimator based on the GP tail limit.@en

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.@en

One of Risso’s dolphin’s distinctive characteristics is the tendency to “lighten” with age due to the accumulation of unpigmented scars. These accumulated scars may provide an indication of age. Photographic skin recaptures gathered from 61 free-ranging animals over a period of 15 years were analyzed to develop a skin classification model in 6 skin stages. Classification of photographic skin captures following this model was tested by 15 experts and 13 nonexpert rankers, with a general probability of agreement of 79%. The duration of each skin stage was estimated using a statistical model based on the recorded dates in which individual animals were known to have entered and/or exited a given stage. A Bayesian approach was used to combine available photographic skin recapture data using expert knowledge as prior to predict the duration for each skin stage and thus the mean age at each stage. Results suggest that animals may live more than 45 years, which is in agreement with published information based on dental layers. The proposed skin stages can be correlated with reproduction, with the transition to stage 3 linked to the onset of maturity. Adult females are less scarified than males and were not observed in the whiter skin classes. The proposed skin stage model is noninvasive and easy to apply and could be a valuable tool in further studies of population structure and dynamics of Risso’s dolphins.@en

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