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information about data such as terrorist attacks. Outlier analysis is especially adequate for fraud detection which is performed by an a nomaly detection mechanism. Network intrusion detection, fraud detection in banking and telecommunications are some of the application areas of outlier detection ( Tang & He, 2017 ). If any data point is extremely different from the whole data in a process, then it is marked as an outlier ( Qi & Chen, 2018 ). Outliers may emerge because of various causes such as malicious attacks, environmental factors, human errors, abnormal conditions

: Data reconciliation and gross error detection. Measurement and Control, 42 (7), 209-210. [11] Koufakou, A., Georgiopoulos, M. (2010). A fast outlier detection strategy for distributed highdimensional data sets with mixed attributes. Data Mining and Knowledge Discovery , 20 (2), 259-289. [12] Wang, Z., Wang, Q., Wang, X. (2011). A novel method of gross error identification in non-diffracting beam triangulation measurement system. In Fourth International Seminar on Modem Cutting and Measurement Engineering, 10-12 December 2010. SPIE, Vol. 7997, 1-6. [13] Qin, P

. Chandola. V., Banerjee, A., Kumar, V. : Anomaly detection – a survey. ACM Comput Surv. 2009, 4 (3), pp. 1–58. 8. Barnett, V., Lewis, T. : Outliers in Statistical Data . John Wiley, 3rd edition 1994. 9. Zhang, Ji. : Advancements of Outlier Detection: A Survey . ICST Transactions on Scalable Information Systems, 2013, 13 (1), pp. 1-26. 10. Muraleedharan, G., Lucas, C., Guedes Soares, C.: Regression quantile models for estimating trends in extreme significant wave heights . J. Ocean Engineering. 2016, 118, pp. 204–215. 11. Zhang, K., Hutter, M., Jin, H. : A new local

., Leroy A. (2003): Robust Regression and Outlier Detection. John Wiley & Sons. Sakamoto Y., Ishiguro M., Kitagawa G. (1986): Akaike Information Criterion Statistics. Tokyo Reidel Publishing Company. Srivastava M.S., Von Rosen D. (1998): Outliers in Multivariate Regression Models. J. Mult. Anal. 65: 195-208. Stefansky W. (1972): Rejecting outliers in factorial designs. Technometrics 14: 469-479.


Anonymous communication networks like Tor are vulnerable to attackers that control entry and exit nodes. Such attackers can compromise the essential anonymity and privacy properties of the network. In this paper, we consider the path bias attack– where the attacker induces a client to use compromised nodes and thus links the client to their destination. We describe an efficient scheme that detects such attacks in Tor by collecting routing telemetry data from nodes in the network. The data collection is differentially private and thus does not reveal behaviour of individual users even to nodes within the network. We show provable bounds for the sample complexity of the scheme and describe methods to make it resilient to introduction of false data by the attacker to subvert the detection process. Simulations based on real configurations of the Tor network show that the method works accurately in practice.

scientific workers, Žilina 2009, p. 109-114, ISBN 978-80-554-0030-3. [9] FILZMOSER, P.: A multivariate outlier detection method. In S. Aivazian, P. Filzmoser, and Yu. Kharin, editors, Proceedings of the Seventh International Conference on Computer Data Analysis and Modelling, volume 1, pp. 18-22, Belarusian State University, Minsk, 2004. [10] SCHAFER, J. L.: Outlier detection and editing procedures for continuous multivariate data. Working paper No. 2008-07. Department of Statistics, Princeton University, 2003, pp. 26. [cit. 09.2014]. Available at: http


An important step in the full definition of an analytical method is the characterization of the within and between laboratory variability. This is typically done through collaborative studies involving multiple laboratories. The statistical analysis of the results of collaborative studies is generally carried out using standardized protocols such as those given in ISO 5725-2 or ASTM E691-14.

One aspect of the evaluation of collaborative studies is the identification of outlying laboratories which are then excluded from the variance calculation associated with the analytical method. Whether particular laboratories are identified as outliers can have a dramatic effect on the calculated variances.

The generally recommended approach to identify laboratories with excessive within-laboratory variation is Cochran’s Test or something similar. However, Cochran’s Test is very sensitive to non-normality of the underlying statistical distribution. When the assumption of normality is violated, Cochran’s Test can wrongly identify laboratories as outliers at much greater than the nominally stated error rate, even for deviations from normality that are very difficult to detect analytically.

In this paper, an alternative to Cochran’s Test, adapted from Levene’s Test, is proposed and shown to approximately maintain the stated error rate when the underlying distribution is not normal. This newly adapted test is recommended for future collaborative study analysis in place of Cochran’s Test.

in two or three-way layouts. Technometrics 23: 65-70. Grubbs F.E. (1950): Sample criteria for testing outlying observations. Ann. Math. Statist. 21: 27-58. Grubbs F.E. (1969): Procedures for detecting outlying observations in samples. Technometrics 11: 1-21. Joshi P.C. (1972): Some slippage tests of mean for a single outlier in linear regression. Biometrika 59: 109-120. Karlin S., Traux D. (1960): Slippage problems. Ann. Math. Statist 31: 296-324. Pan J.X., Fang K.T. (1995): Multiple outlier detection in growth curve model with unstructured covariance matrix. Ann


The average expected duration of human life is rising because of different reasons. On the other hand, not only the duration, but the quality of life level is important, too. The higher the quality of life level, the citizens’ happiness and satisfaction levels are higher, which has positive impact on the development and operating of an economy. The goal of this paper is to identify groups of European countries, using statistical hierarchical cluster analysis, by using the quality of life indicators, and to recognise differences in quality of life levels. The quality of life is measured by using seven different indicators. The conducted statistical hierarchical cluster analysis is based on the Ward’s clustering method, and squared Euclidean distances. The results of conducted statistical hierarchical cluster analysis enabled recognizing of three different groups of European countries: old European Union member states, new European Union members, and non-European Union member states. The analysis has revealed that the old European Union member states seem to have in average higher quality of life level than the new European Union member states. Furthermore, the European Union member states have in average higher quality of live level than non-European Union members do. The results indicate that quality of life levels and economic development levels are connected.

components: Primary theory and Monte Carlo, Journal of the American Statistical Association 80(391): 759-766. Li W. and Qin S. J. (2001). Consistent dynamic PCA based on errors-in-variables subspace identification, Journal of Process Control 11(6): 661-678. Maronna R. A., Martin R. and Yohai V. J. (2006). Robust Statistics: Theory and Methods , Wiley, New York, NY. Qin S. J. (2003). Statistical process monitoring: Basics and beyond, Journal of Chemometrics 17(8-9): 480-502. Rousseeuw P. (1987). Robust Regression and Outliers Detection , Wiley, New York, NY