Improving extreme quantile estimation via a folding procedure

In many applications (geosciences, insurance, etc.), the peaks-over-thresholds (POT) approach is one of the most widely used methodology for extreme quantile inference. It mainly consists of approximating the distribution of exceedances above a high threshold by a generalized Pareto distribution (GPD). The number of exceedances which is used in the POT inference is often quite small and this leads typically to a high volatility of the estimates. Inspired by perfect sampling techniques used in simulation studies, we define a folding procedure that connects the lower and upper parts of a distribution. A new extreme quantile estimator motivated by this theoretical folding scheme is proposed and studied. Although the asymptotic behaviour of our new estimate is the same as the classical (non-folded) one, our folding procedure reduces significantly the mean squared error of the extreme quantile estimates for small and moderate samples. This is illustrated in the simulation study. We also apply our method to an insurance dataset.     

Goodness-of-fit testing for Weibull-type behavior

In the process of analyzing data, testing the fit of a model under consideration is a prerequisite for performing inference about the model parameters. In this paper we examine the goodness-of-fit testing problem for assessing whether a sample is consistent with the Weibull-type model. Inspired by the Jackson and the Lewis test statistics, originally proposed as goodness-of-fit tests for the exponential distribution, we introduce two new statistics for testing Weibull-type behavior, and study their asymptotic properties. Moreover, given that the statistics are ratios of estimators for the Weibull-tail coefficient, we obtain new estimators for the latter, and establish their consistency and asymptotic normality. The small sample behavior of our statistics and estimators is evaluated on the basis of a simulation study.     

Alien plant species do have a clear preference for different land uses within urban environments

Since neophytes can become invasive in the future, untangling their ecological preferences is of paramount importance, especially in urban areas where they represent a substantial proportion of the local flora. Studies exploring alien species assemblages in urban environments are however scarce. This study aims to unravel alien plant species preferences for five urban land uses (densely built-up areas, open built-up areas, industrial areas, broadleaved urban forests, and agricultural areas and small landscape elements). We took the city of Brussels as a model, in which we recorded all vascular species growing spontaneously in grid cells of 1 km². We tested two different ways of classifying the 1-km² cells: (1) We simply associated each cell with its dominant land cover; (2) We used a fuzzy approach for which the degree of association of a given cell to a given land cover depended on the proportion of that land cover within the cell. For both classification methods, we calculated the indicator species of the resulting land cover types based on alien species only. The crisp and fuzzy classifications identified 33 and 49 species, respectively, with a clear preference for some urban land use types (from a total of 129 alien plant species analyzed). Results showed that urban land use types having apparently similar environmental conditions can actually harbor different neophyte assemblages. Fine-tuning the categorization of urban environments in future ecological studies is therefore important for understanding spatial patterns of alien species occurrence.     

The Theory of Conditionality: An Illustration of the Place of Norms in the Field of Social Thinking

In the field of the central core theory of social representations, research which has focused on the normative aspects is relatively recent as it dates back little more than ten years. The theory of conditionality which developed from research into the periphery of representation results from this. It is a particularly fruitful theory to explain “normative latitudes” and the behaviour accruing to them. One of the particularities of these works stresses the importance of linking the normative aspects with specific methods and/or analyses. In this paper, we will illustrate it via a specific tool developed in the field of traffic psychology: the Conditional Script Questionnaire (CSQ). This approach makes it possible to highlight the interactions between two systems of norms: the legal system and the social system. The implication of norms is fundamental in different processes already studied such as social influence or identity processes, and this article can be considered as an illustration of the place of norms in the field of social thinking.     

Bias-reduced extreme quantile estimators of Weibull tail-distributions

In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an exponential regression model that was introduced in Diebolt et al. [2007. Bias-reduced estimators of the Weibull-tail coefficient. Test, to appear]. The asymptotic normality of the extreme quantile estimator is established. We also introduce an adaptive selection procedure to determine the number of upper order statistics to be used. A simulation study as well as an application to a real data set is provided in order to prove the efficiency of the above-mentioned methods.     

A diagnostic for selecting the threshold in extreme value analysis

A new approach is suggested for choosing the threshold when fitting the Hill estimator of a tail exponent to extreme value data. Our method is based on an easily computed diagnostic, which in turn is founded directly on the Hill estimator itself, 'symmetrized' to remove the effect of the tail exponent but designed to emphasize biases in estimates of that exponent. The attractions of the method are its accuracy, its simplicity and the generality with which it applies. This generality implies that the technique has somewhat different goals from more conventional approaches, which are designed to accommodate the minor component of a postulated two-component Pareto mixture. Our approach does not rely on the second component being Pareto distributed. Nevertheless, in the conventional setting it performs competitively with recently proposed methods, and in more general cases it achieves optimal rates of convergence. A by-product of our development is a very simple and practicable exponential approximation to the distribution of the Hill estimator under departures from the Pareto distribution.