On Tail Index Estimation based on Multivariate Data

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate Central Limit Theorem for a random vector, whose components correspond to (possibly dependent) Hill estimators of the common shape index alpha, is established under mild conditions. Motivated by the statistical analysis of extremal spatial data in particular, we introduce the concept of (standard) heavy-tailed random field of tail index alpha and show how this limit result can be used in order to build an estimator of alpha with small asymptotic mean squared error, through a proper convex linear combination of the coordinates. Beyond asymptotic results, simulation experiments illustrating the relevance of the approach promoted are also presented

Sloshing in the LNG shipping industry: risk modelling through multivariate heavy-tail analysis

In the liquefied natural gas (LNG) shipping industry, the phenomenon of sloshing can lead to the occurrence of very high pressures in the tanks of the vessel. The issue of modelling or estimating the probability of the simultaneous occurrence of such extremal pressures is now crucial from the risk assessment point of view. In this paper, heavy-tail modelling, widely used as a conservative approach to risk assessment and corresponding to a worst-case risk analysis, is applied to the study of sloshing. Multivariate heavy-tailed distributions are considered, with Sloshing pressures investigated by means of small-scale replica tanks instrumented with d >1 sensors. When attempting to fit such nonparametric statistical models, one naturally faces computational issues inherent in the phenomenon of dimensionality. The primary purpose of this article is to overcome this barrier by introducing a novel methodology. For d-dimensional heavy-tailed distributions, the structure of extremal dependence is entirely characterised by the angular measure, a positive measure on the intersection of a sphere with the positive orthant in Rd. As d increases, the mutual extremal dependence between variables becomes difficult to assess. Based on a spectral clustering approach, we show here how a low dimensional approximation to the angular measure may be found. The nonparametric method proposed for model sloshing has been successfully applied to pressure data. The parsimonious representation thus obtained proves to be very convenient for the simulation of multivariate heavy-tailed distributions, allowing for the implementation of Monte-Carlo simulation schemes in estimating the probability of failure. Besides confirming its performance on artificial data, the methodology has been implemented on a real data set specifically collected for risk assessment of sloshing in the LNG shipping industry

Sloshing in the shipping industry: risk modelling through multivariate heavy-tail analysis

International audienceIn the liquefied natural gas (LNG) shipping industry, the phenomenon of sloshing can lead to the occurrence of very high pressures in the tanks of the vessel. The issue of modelling or estimating the probability of the simultaneous occurrence of such extremal pressures is now crucial from the risk assessment point of view. In this paper, heavy-tail modelling, widely used as a conservative approach to risk assessment and corresponding to a worst-case risk analysis, is applied to the study of sloshing. Multivariate heavy-tailed distributions are considered, with Sloshing pressures investigated by means of small-scale replica tanks instrumented with d >1 sensors. When attempting to fit such nonparametric statistical models, one naturally faces computational issues inherent in the phenomenon of dimensionality. The primary purpose of this article is to overcome this barrier by introducing a novel methodology. For d-dimensional heavy-tailed distributions, the structure of extremal dependence is entirely characterised by the angular measure, a positive measure on the intersection of a sphere with the positive orthant in Rd. As d increases, the mutual extremal dependence between variables becomes difficult to assess. Based on a spectral clustering approach, we show here how a low dimensional approximation to the angular measure may be found. The nonparametric method proposed for model sloshing has been successfully applied to pressure data. The parsimonious representation thus obtained proves to be very convenient for the simulation of multivariate heavy-tailed distributions, allowing for the implementation of Monte-Carlo simulation schemes in estimating the probability of failure. Besides confirming its performance on artificial data, the methodology has been implemented on a real data set specifically collected for risk assessment of sloshing in the LNG shipping industry

Primary localized rectal/pararectal gastrointestinal stromal tumors: results of surgical and multimodal therapy from the French Sarcoma group.

BACKGROUND: Rectal and pararectal gastrointestinal stromal tumors (GISTs) are rare. The optimal management strategy for primary localized GISTs remains poorly defined. METHODS: We conducted a retrospective analysis of 41 patients with localized rectal or pararectal GISTs treated between 1991 and 2011 in 13 French Sarcoma Group centers. RESULTS: Of 12 patients who received preoperative imatinib therapy for a median duration of 7 (2-12) months, 8 experienced a partial response, 3 had stable disease, and 1 had a complete response. Thirty and 11 patients underwent function-sparing conservative surgery and abdominoperineal resection, respectively. Tumor resections were mostly R0 and R1 in 35 patients. Tumor rupture occurred in 12 patients. Eleven patients received postoperative imatinib with a median follow-up of 59 (2.4-186) months. The median time to disease relapse was 36 (9.8-62) months. The 5-year overall survival rate was 86.5%. Twenty patients developed local recurrence after surgery alone, two developed recurrence after resection combined with preoperative and/or postoperative imatinib, and eight developed metastases. In univariate analysis, the mitotic index (≤5) and tumor size (≤5 cm) were associated with a significantly decreased risk of local relapse. Perioperative imatinib was associated with a significantly reduced risk of overall relapse and local relapse. CONCLUSIONS: Perioperative imatinib therapy was associated with improved disease-free survival. Preoperative imatinib was effective. Tumor shrinkage has a clear benefit for local excision in terms of feasibility and function preservation. Given the complexity of rectal GISTs, referral of patients with this rare disease to expert centers to undergo a multidisciplinary approach is recommended