Nonparametric estimation of extremal dependence

There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a multivariate distribution by modelling the marginal distributions and the dependence structure separately. For estimating dependence at high levels, the stable tail dependence function and the spectral measure are particularly convenient. These objects also lie at the basis of nonparametric techniques for modelling the dependence among extremes in the max-domain of attraction setting. In case of asymptotic independence, this setting is inadequate, and more refined tail dependence coefficients exist, serving, among others, to discriminate between asymptotic dependence and independence. Throughout, the methods are illustrated on financial data.Comment: 22 pages, 9 figure

Sedimentary deposits and bioturbation in an Early Cretaceous subarctic stormy greenhouse shelf environment

This study of the Aptian lower part of the Carolinefjellet Formation in Svalbard, Norwegian high Arctic, is based on well cores and outcrop section in the Adventdalen area of Spitsbergen and reports on the deposits and bioturbation structures of an ancient subpolar marine shelf from a well-known period of global greenhouse climate. The study documents the sedimentation conditions and benthic fauna activity on a warm-water aggrading shelf subject to harsh Arctic wave climate and eurybatic base-level changes, with episodic bottom incursions of cold polar water. Lithofacies associations and 38 observed ichnotaxa represent subenvironments ranging from offshore to lower shoreface and hosting the Cruziana ichnofacies in its distal to proximal expression, with a brief mid-Aptian encroachment of middle shoreface zone with a distal expression of the Skolithos ichnofacies. The ichnofacies are variously impoverished compared to their archetypes. The sediment bioturbation intensity varies, but similar lithofacies associations show a comparable intensity throughout the stratigraphic succession, which indicates an ichnofauna ecology controlled by the seafloor hydraulic regime and oxygenation, and thus mainly by the wave climate and relative sea-level changes. Sandstone tempestites indicate high-frequency storms, commonly exceeding the magnitude of largest modern hurricane events. The study confirms that a change in global climate mode, such as the Early Cretaceous warming, entails extreme weather conditions.publishedVersio

Mathematical techniques for the protection of patient's privacy in medical databases

In modern society, keeping the balance between privacy and public access to information is becoming a widespread problem more and more often. Valid data is crucial for many kinds of research, but the public good should not be achieved at the expense of individuals. While creating a central database of patients, the CSIOZ wishes to provide statistical information for selected institutions. However, there are some plans to extend the access by providing the statistics to researchers or even to citizens. This might pose a significant risk of disclosure of some private, sensitive information about individuals. This report proposes some methods to prevent data leaks. One category of suggestions is based on the idea of modifying statistics, so that they would maintain importance for statisticians and at the same time guarantee the protection of patient's privacy. Another group of proposed mechanisms, though sometimes difficult to implement, enables one to obtain precise statistics, while restricting such queries which might reveal sensitive information

Nonparametric modeling of extremal dependence

There is an increasing interest to understand the interplay of extreme values over time and across coordinates. Extreme-value theory provides techniques for modeling temporal and cross-sectional extremal dependence by modeling the marginal distributions and the dependence structure separately. Regular variation is the key assumption in this context. Inference about serial extremal dependence within a time series can be made via the spectral tail process. For estimating dependence at high levels within a multivariate random vector, the spectral measure is particularly convenient. The aim of this thesis is to extend the statistical toolbox for modeling extremal dependence in space or time. In particular, the focus is on nonparametric techniques for estimating the spectral tail process and the spectral measure. Appropriate estimators are constructed and their large-sample distribution is derived. Their finite-sample performance is evaluated via Monte Carlo simulations. Throughout the theory is illustrated on financial or weather data.(SC - Sciences) -- UCL, 201

Nonparametric Estimation of Extremal Dependence

There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a multivariate distribution by modelling the marginal distributions and the dependence structure separately. For esti- mating dependence at high levels, the stable tail dependence function and the spectral measure are particularly convenient. These objects also lie at the basis of nonpara- metric techniques for modelling the dependence among extremes in the max-domain of attraction setting. In case of asymptotic independence, this setting is inadequate, and more refined tail dependence coefficients exist, serving, among others, to discrim- inate between asymptotic dependence and independence. Throughout, the methods are illustrated on financial data

Modeling serial extremal dependence

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warchol [Extremes (2015) 18, 369-402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended to the more general setting of a stationary, regularly varying time series. The large-sample distribution of the estimators is derived via empirical process theory for cluster functionals. The finite-sample performance of these estimators is evaluated via Monte Carlo simulations. Moreover, two different bootstrap schemes are employed which yield confidence intervals for the pre-asymptotic spectral tail process: the stationary bootstrap and the multiplier block bootstrap. The estimators are applied to stock price data to study the persistence of positive and negative shocks