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Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators
Kalina, Jan
The paper is devoted to highly robust statistical estimators based on implicit weighting, which have a potential to find econometric applications. Two particular methods include a robust correlation coefficient based on the least weighted squares regression and the minimum weighted covariance determinant estimator, where the latter allows to estimate the mean and covariance matrix of multivariate data. New tools are proposed allowing to test hypotheses about these robust estimators or to estimate their variance. The techniques considered in the paper include resampling approaches with or without replacement, i.e. permutation tests, bootstrap variance estimation, and bootstrap confidence intervals. The performance of the newly described tools is illustrated on numerical examples. They reveal the suitability of the robust procedures also for non-contaminated data, as their confidence intervals are not much wider compared to those for standard maximum likelihood estimators. While resampling without replacement turns out to be more suitable for hypothesis testing, bootstrapping with replacement yields reliable confidence intervals but not corresponding hypothesis tests.
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Correlation coefficients and their field of application
Rudžík, Matej ; Popela, Pavel (referee) ; Žák, Libor (advisor)
This bachelor’s thesis deals with different types of correlation coefficients and their properties depending on the data layout. The theoretical part of this work contains definitions of various types of correlation coefficients and tests related with this issue. The practical part compares the behaviour of parametric and nonparametric correlation coefficients in different situations. This comparison is realised in program MATLAB.
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Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators
Kalina, Jan
The paper is devoted to highly robust statistical estimators based on implicit weighting, which have a potential to find econometric applications. Two particular methods include a robust correlation coefficient based on the least weighted squares regression and the minimum weighted covariance determinant estimator, where the latter allows to estimate the mean and covariance matrix of multivariate data. New tools are proposed allowing to test hypotheses about these robust estimators or to estimate their variance. The techniques considered in the paper include resampling approaches with or without replacement, i.e. permutation tests, bootstrap variance estimation, and bootstrap confidence intervals. The performance of the newly described tools is illustrated on numerical examples. They reveal the suitability of the robust procedures also for non-contaminated data, as their confidence intervals are not much wider compared to those for standard maximum likelihood estimators. While resampling without replacement turns out to be more suitable for hypothesis testing, bootstrapping with replacement yields reliable confidence intervals but not corresponding hypothesis tests.
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Tests for Combination of Correlation Coefficients
Kulíšková, Michaela ; Hudecová, Šárka (advisor) ; Pešta, Michal (referee)
This bachelor thesis is focused on tests for correlation coefficients. Fundamental knowledge about correlation coefficient are reminded as well as tests for correlation coefficient based on estimated correlation coefficient. Then three main methods for combining more correlation coefficients - Fisher`s method, Linear combination test with Z-transformation and Hotelling transformation - are described, simulated and compared. These tests have several assumptions such as that k correlation coefficients are known as well as the range of random samples from which they were calculated plus it is assumed that these correlation coefficients are equal.
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Nonparametric tests of independence
Kmeťková, Diana ; Pawlas, Zbyněk (advisor) ; Hlubinka, Daniel (referee)
The main objective of this thesis is the presentation regarding the problem of testing independence between two random variables in the nonparametric model of continuous cumulative distribution functions. Firstly, the reader is informed with basic notions from the theory of independence and rank tests. Afterwards, few of the most common methods for testing independence are introduced. In the beginning, the test based on Pearson's correlation coefficient is mentioned as a representative for parametric tests, then we continue with nonparametric tests, such as test based on Spearman's, Kendall's and distance correlation coefficient. We focus in better detail on Hoeffding's test of independence, which results to be consistent against all alternatives in the model of continuous cumulative distribution functions. In the end, we compare and evaluate presented methods for testing independence using simulations in R environment.
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Comparison of signatures using metrics for the eye movements
Vyhlas, Petr ; Děchtěrenko, Filip (advisor) ; Gemrot, Jakub (referee)
Comparison of signatures is part of the identity verification. The study focuses on comparison of signatures using metrics for the eye movements. In first part of study we review algorithms for the signature verification and we introduce metrics for comparing eye movements. We used Levenshtein distance, Fréchet distance and correlation coefficient for the comparison of signatures. We discovered behavior of these metrics and choose their combination for the computation of percentage similarity between two signatures. We designed and implemented universal Windows application which digitizes signatures, compares two signatures and determines their similarity. We conducted an experiment in which participants tried to sign themselves or tried to sign someone else. We did not find improvement during the signing. Powered by TCPDF (www.tcpdf.org)
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Analysis of general and specific physical conditioning tests in youth Nordic skiers and biathletes
Korbelář, Tomáš ; Sucharda, Jan (advisor) ; Gnad, Tomáš (referee)
Title: Analysis of general and specific physical conditioning tests in youth Nordic skiers and biathletes. Goal: The goal of thesis is judge the validity of individual general and specific physical conditioning tests in 2012, 2013 and 2014 and compare this way the youth categories in Nordic skiing and biathlon. Methods: From the test results of general and specific physical conditioning tests and results of the czech cup youth ranking as an index fo achievement in Nordic skiing and biathlon we did a correlation analysis to figure out the extent of dependence. With the help of correlation analysis we came to the conclusion that the tests in biathlon show stronger correlation to achievement than tests in Nordic skiing. Nordic skiing, biathlon, czech cup ranking, youth - male, female, correlation, coefficient, test sets, achievement, prediction, train-ability Results: Keywords:
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Dependence of the position of teams in the FIFA rankings on the achievements in top tournaments
Kotrba, Lukáš ; Šíma, Jan (advisor) ; Omcirk, Vilém (referee)
Title: Dependence of the position of teams in the FIFA rankings on the achievements in top tournaments Objectives: The aim of this work is determining dependency team standings in the FIFA rankings on the achievements in top tournaments. This is the World Cup in 1998, 2002, 2006, 2010 and 2014. Methods: In my thesis I used a method of regression and correlation analysis, correlation coefficient and regression straight line. Results: All results are presented in the analytical part of the work. It was found dependency between the observed data and an increasing trend. The biggest dependence was at the World Cup 2014, which reached high levels. The smallest was at the World Cup 1998 and 2002, where the results reached below average. Keywords: Football, FIFA, FIFA World rankings, FIFA World Cup, correlation analysis, regression analysis, correlation coefficient, regression straight line
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Pearsonův correlation coefficient and its use in statistical inference
Németh, Richard ; Omelka, Marek (advisor) ; Maciak, Matúš (referee)
The main objective of this thesis is to determine asymptotic distribution of sample correlation coefficient without the assumption of normal distribution and its effects on commonly used sta- tistical tests of independence and confidence intervals for correlation coefficient. The problem is solved by central limit theorem and delta method. We have shown that the commonly used statis- tical tests for independence in practice are valid, even without the assumption of normal distribu- tion. We have also derived more versions of statistical tests for independence of random variables and more versions of confidence intervals for correlation coefficient without the assumption of normality. In conclusion we have compared individual statistical tests and confidence intervals for specific multivariate distributions using simulations. 1
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