No abstract

No abstract

We 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 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.

No abstract

Healthcare quality monitoring by the Ministry of Health in Slovenia includes over 100 business indicators of economy, efficiency and funding allocation, which are analysed annually for over 20 hospitals. Most of these indicators are random‐denominator same‐quantity ratios with a strongly correlated numerator and denominator, and the goal is the identification of outliers. A large simulation study was performed to study the performance of three types of methods: common outlier detection tests for small samples—Grubbs, Dean and Dixon, and Nalimov tests—applied unconditionally and conditionally upon results of Shapiro–Wilk normality test; the boxplot rule; and the double‐square‐root control chart, for which we introduced regression‐through‐origin‐based control limits. Pert, Burr and three‐parameter loglogistic distributions, which fitted the real data best, were used with no, one or two outliers in the simulated samples of sizes 5 to 30. Small (below 0.2, right skewed) and large (above 0.5, more symmetrical) ratios were simulated. Performance of the methods varied greatly across the conditions. Formal small‐sample tests proved virtually useless if applied conditionally upon passed normality pre‐test in the presence of outliers. Boxplot rule performed most variedly but was the only useful one for tiny samples. Our variant of the double‐square‐root control chart proved too conservative in tiny samples and too liberal for samples of size 20 or more without outliers but appeared the most useful to detect actual outliers in samples of the latter size. As a possibility for future improvement and research, we propose pre‐testing of normality by using a class of robustified Jarque–Bera tests. Copyright © 2011 John Wiley & Sons, Ltd.