Luboš Střelec

Small Sample Robust Testing for Normality against Pareto Tails

The aim of this article is to introduce the general form (so called RT class) of the robust and classical Jarque–Bera (JB) test based on the location functional. We introduce the two-step procedure which is optimal for testing against the individual or contaminated Pareto alternative. As a reference for such a contamination we consider different Pareto distributions. We also give practical guidelines for robust testing for normality against short- and heavy-tailed alternatives. We concentrate mainly on simulation results for moderate and small samples. However, we also prove consistency and asymptotic distribution for introduced tests. We show that as the suitable measure of nominal level of Pareto tail parameter we may take the t-Hill estimator introduced in the article. To guarantee the consistency of the whole procedure, we also prove the consistency of t-Hill estimator. The introduced general class of robust tests of the normality is illustrated at the selected datasets of financial time series.

On simulation of exact tests in Rayleigh and normal families

The aim of this article is to discuss homogeneity testing of the Rayleigh distribution and relate it to homogeneity testing in exponential family. In particular, we simulate and discuss the power of exact likelihood ratio test of homogeneity against the three-components subpopulation alternative (ELR3). This article also deals with robust testing for normality. We introduce the general RT class of robust tests for normality and present and discuss the power of selected RT tests against alternative distributions that are known to be problematic for the Jarque-Bera test - bimodal, uniform and Weibull alternatives.

Geometric aspects of robust testing for normality and sphericity

ABSTRACT 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 p-values, effect sizes, and confidence intervals. Therefore, quite naturally, research on robust testing for normality has become a new trend. Robust testing for normality can have counterintuitive behavior, some of the problems have been introduced in Stehlík et al. [Chemometrics and Intelligent Laboratory Systems 130 (2014): 98–108]. Here we concentrate on explanation of small-sample effects 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.

Comparison and Modelling of Pension Systems

The purpose of this work is a comparison of pension systems of the selected countries—the pension systems and reforms of Austria, the Czech Republic, Slovakia, Sweden, Poland, and Chile will be our subjects of interest. Firstly, we focus on a short historical overview of the development and classification of pension systems in general. Consequently, the main part of this chapter deals with different scenarios, which should show whether the systems would be stable in the future. For these purposes, we developed utility in Mathematica. We tested normality of salary samples from Slovakia by robust tests for normality and computed pensions in several scenarios.

Alternative Approaches for Assessing the European Countries Economic and Social Results

Abstract The European Union has been passing a complicated period over the last years. The EU economy lags behind its own development goals as well as, behind the results achieved by its economic partners and competitors – USA and Japan. Due to lower competitiveness in the international market environment, the persisting or even expanding problems on the domestic labor markets are evident. Many EU countries demonstrate relatively high unemployment which leads to weakening the income situation of households and strengthening the social tension in society. Particularly worrying is situation of young graduates and also people approaching retirement age and seniors. In context of such arguments, the strategy for perspective development of the EU – the strategic document Europe2020 – has been proposed. Its key objective is to strengthen the economic competitiveness of the European Union, its member countries and particularly the competitiveness of its firms. It is expected that the Europe 2020 objectives will create favorable environment for reducing the social tension across the EU countries and finally lead to the better life of majority of its citizens. All the EU2020 goals are difficult. To achieve them it is necessary to identify precisely the current positions of individual countries and their distances from these ambitious goals in order to select the optimal strategies to their fulfillment. Our paper aims to contribute to identification of the current competitiveness position of the EU and its member states in international market environment and to estimate the chances for achieving the EUROPE 2020 strategic goals.

On power comparison of normality tests of error terms in regression models

Verification of regression models constitutes one of the most important steps in applied regression analysis and is primarily based on analysis of error terms. Some statistical procedures used in the testing of linear regression model such as t-test or F-test are based on assumption of normality of error terms. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques. This contribution aims at assessment of a power of several robust and non-robust normality tests of error terms in regression models. For this purpose using a Monte Carlo simulation technique we simulate the dependent variable by p-location outlier models and estimate the ordinary least square residuals. Finally we test the normality of residuals to explore the power and robustness of selected robust and non-robust normality tests.

Performance of the OLS estimator in presence of autocorrelation

In this paper we show behaviour of some estimators for linear panel data models with autocorrelated idiosyncratic noise. This contribution then discusses properties of widely used estimators as ordinary least square, and Prais-Winsten estimator, respectively, in case of temporally correlated panel data. By a Monte Carlo study we assess the bias and efficiency of the correction methods under different data generating processes. Using Monte Carlo simulation we investigate how the performance of the OLS and GLS estimators varies according to increasing dependence in time dimension, i.e. we expect an increasing bias of the OLS estimator as temporal correlation augments.

Robust testing for normality of error terms with presence of autocorrelation and conditional heteroscedasticity

Normality of the error terms in regression models is one of the basic assumptions in the applied regression analysis. Therefore, testing for normality of the error terms constitutes one of the most important steps of regression model verification and validation. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Within the applied regression analysis there is a frequent problem of the presence of autocorrelation and conditional heteroscedasticity of the error terms. Under both autocorrelation and heteroscedasticity, the usual OLS estimators are still unbiased, linear and asymptotically normally distributed, however, no longer have the minimum variance property among all linear unbiased estimators.Therefore, the aim of this paper is to present and discuss normality testing of the error terms with presence of autocorrelation and conditional heteroscedasticity. To explore the power of selected classical tests and robust tests for normality, we perform simulation study.Normality of the error terms in regression models is one of the basic assumptions in the applied regression analysis. Therefore, testing for normality of the error terms constitutes one of the most important steps of regression model verification and validation. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Within the applied regression analysis there is a frequent problem of the presence of autocorrelation and conditional heteroscedasticity of the error terms. Under both autocorrelation and heteroscedasticity, the usual OLS estimators are still unbiased, linear and asymptotically normally distributed, however, no longer have the minimum variance property among all linear unbiased estimators.Therefore, the aim of this paper is to present and discuss normality testing of the error terms with presence of autocorrelation and conditional heteroscedasticity. To explore the power of selected classical tests an...

Sustainable Development in the EU

The challenges of globalisation, technological progress and limited world resources that are typical of elevated consumption must be necessarily addressed in a manner that reflects both socio-economic and environmental problems. One relevant approach to these problems is represented by so-called sustainable economics. This approach cannot address traditional measures of economic performance such as GDP or GNP and requires a new methodology for the measurement of socio-economic activities in the environmental context. In this chapter, we present widely used indicators of sustainable development, namely, the Better Life Index, the Ecological Footprint, the Happy Planet Index, and the Environmental Performance Index. The content and appropriate uses of these indices in the EU countries are discussed, devoting special attention to the CEE countries. We also investigate relationships among those indices. Based on a quantitative analysis, we identify clusters of EU countries with similar levels of sustainable development. Furthermore, we classify the EU countries according to their effective use of natural resources relative to economic output.

Selected issues on robust testing for normality

Normal distribution is mostly used distribution in statistics, dating back to the Karl F. Gauss. It is used in many branches of statistics, however, testing for normality is not well understood. But which deviations from theoretical normality are still acceptable for a given statistical procedure? This contribution aims towards better understanding of such problems. In particular, we study how much effects the violation of ANOVA prerequisites the underlying inference. It is clear, that one should develop a proper robustness in a given setup, under which the statistical analysis is still reliable. We also study the influence of outliers in dataset, in particular with focus on the tradeoff between power and robustness.