 

HardyWeinberg equlibrium
Vlčková, Katarína ; Zvára, Karel (advisor) ; Kulich, Michal (referee)
In this paper, we describe various tests used to determine deviations from the HardyWeinberg equilibrium. The tests described are: the exact test, the χ2 test with and without continuity correction, the conditional χ2 test with and without continuity correction and the likelihood ratio test. These tests explore the question whether a random sample has trinomic distribution with probabilities pAA = θ2 , pAa = 2θ(1 − θ), paa = (1 − θ)2 . In this work, we simulate data of sample size 100 and we estimate the probability of type I error and the power of the tests. In this case, we get the best results with conditional χ2 test. The estimate of the power of the likelihood ratio test and the χ2 test is one of the highest of all. On the other hand, these two test are anticonservative in some cases . 1


Highly Robust Estimation of the Autocorrelation Coefficient
Kalina, Jan ; Vlčková, Katarína
The classical autocorrelation coefficient estimator in the time series context is very sensitive to the presence of outlying measurements in the data. This paper proposes several new robust estimators of the autocorrelation coefficient. First, we consider an autoregressive process of the first order AR(1) to be observed. Robust estimators of the autocorrelation coefficient are proposed in a straightforward way based on robust regression. Further, we consider the task of robust estimation of the autocorrelation coefficient of residuals of linear regression. The task is connected to verifying the assumption of independence of residuals and robust estimators of the autocorrelation coefficient are defined based on the DurbinWatson test statistic for robust regression. The main result is obtained for the implicitly weighted autocorrelation coefficient with small weights assigned to outlying measurements. This estimator is based on the least weighted squares regression and we exploit its asymptotic properties to derive an asymptotic test that the autocorrelation coefficient is equal to 0. Finally, we illustrate different estimators on real economic data, which reveal the advantage of the approach based on the least weighted squares regression. The estimator turns out to be resistant against the presence of outlying measurements.


Robust Regularized Cluster Analysis for HighDimensional Data
Kalina, Jan ; Vlčková, Katarína
This paper presents new approaches to the hierarchical agglomerative cluster analysis for highdimensional data. First, we propose a regularized version of the hierarchical cluster analysis for categorical data with a large number of categories. It exploits a regularized version of various test statistics of homogeneity in contingency tables as the measure of distance between two clusters. Further, our aim is cluster analysis of continuous data with a large number of variables. Various regularization techniques tailormade for highdimensional data have been proposed, which have however turned out to suffer from a high sensitivity to the presence of outlying measurements in the data. As a robust solution, we recommend to combine two newly proposed methods, namely a regularized version of robust principal component analysis and a regularized Mahalanobis distance, which is based on an asymptotically optimal regularization of the covariance matrix. We bring arguments in favor of the newly proposed methods.
