5 research outputs found
Geometric aspects of robust testing for normality and sphericity
Stochastic Robustness of Control Systems under random excitation motivates challenging
developments in geometric approach to robustness. The assumption of normality
is rarely met when analyzing real data and thus the use of classic parametric
methods with violated assumptions can result in the inaccurate computation of pvalues,
e↵ect sizes, and confidence intervals. Therefore, quite naturally, research on
robust testing for normality has become a new trend. Robust testing for normality
can have counter-intuitive behavior, some of the problems have been introduced in
[46]. Here we concentrate on explanation of small-sample e↵ects of normality testing
and its robust properties, and embedding these questions into the more general question
of testing for sphericity. We give geometric explanations for the critical tests. It
turns out that the tests are robust against changes of the density generating function
within the class of all continuous spherical sample distributions
Weak properties and robustness of t-Hill estimators
International audienceWe describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly varying tail. t-Hill estimator is distribution sensitive, thus it differs in e.g. Pareto and log-gamma case. Here, we study both forms of the estimator, i.e. t-Hill and t-lgHill. For both estimators we prove weak consistency in moving average settings as well as the asymptotic normality of t-lgHill estimator in iid setting. In cases of contamination with heavier tails than the tail of original sample, t-Hill outperforms several robust 2 P. Jordanova et al. tail estimators, especially in small samples. A simulation study emphasizes the fact that the level of contamination is playing a crucial role. The larger the contamination, the better are the t-score moment estimates. The reason for this is the bounded t-score of heavy-tailed distributions (and, consequently, bounded influence functions of the estimators). We illustrate the developed methodology on a small sample data set of stake measurements from Guanaco glacier in Chile
Priority statement and some properties of t-lgHill estimator
We acknowledge the priority on the introduction of the formula of t-lgHill estimator for the positive extreme value index. We provide a novel motivation for this estimator based on ecologically driven dynamical systems. Another motivation is given directly by applying the general t-Hill procedure to log-gamma distribution. We illustrate the good quality of t-lgHill estimator in comparison to classical Hill estimator on the novel data of the concentration of arsenic in drinking water in the rural area of the Arica and Parinacota Region, Chile