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Procedures for statistical control of random processes
Lebeda, Matěj ; Antoch, Jaromír (advisor) ; Hušková, Marie (referee)
Procedures for statistical control of random processes are well known. What we miss, is the comparison of such procedures. In the beginning, we will introduce the linear regression model which will be our assumption throughout the whole thesis. Then we will explain three most common violations of the model whereas two of them will be studied closely. In practice, two fundamental approaches are employed: offline and online approach. The offline methods are performed ex-post. We will propose procedures leaning on the assumption of normality, but robust procedures as well. Online methods (so called sequential) are based on a different principle. The most common are Shewhart's and CUSUM method. Finally, the last fifth chapter will be dedicated to comparison of these methods. Our main interests are to detect as fast as possible but also not before the time of change. The approaches will be compared from these aspects. 1
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Tests of independence for functional data
Horská, Šárka ; Hlávka, Zdeněk (advisor) ; Hušková, Marie (referee)
This thesis deals with tests of serial independence for functional time series. The first part of the thesis introduces the issue of serial independence in time series of random vari- ables. The second part focuses on tests of serial independence for functional observations. It examines a test based on autocorrelation and, in particular, a test whose test statistic is derived directly from the definition of independence. This test is modified to a test with a weaker alternative of sub-dependence. The thesis concludes with a comparison of these three tests, which is based on a simulation. 1
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Dynamic panel data models
Lipavská, Kateřina ; Hudecová, Šárka (advisor) ; Hušková, Marie (referee)
This thesis deals with a dynamic panel data model and parameters estimation in these models. First, estimation of parameters in linear regression models is revised as well as ge- neralized method of moments. Second, classical estimation methods for panel data model are considered and it is shown why they are inappopriate to use for dynamic panel data model. Subsequently, two-stage least squares estimation method and estimators based on generalized method of moments are presented, namely Arellano-Bond, Arellano-Bover and Ahn-Schmidt estimators. Some of the theoretical results are illustrated in a Monte Carlo simulation study, which also compares behaviour of the presented estimators under various settings. 1
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Generalized Method of Moments
Volejníková, Viktorie ; Maciak, Matúš (advisor) ; Hušková, Marie (referee)
The topic of this bachelor thesis is the Generalized Method of Moments (GMM), its asymptotic properties, and its implementations. The first chapter briefly introduces the moment conditions and the Method of Moments (MM) which is then generalized to the GMM. In the second chapter, the consistency and the asymptotic normality of the GMM are proved and the optimal weight- ing matrix of the estimator is derived. The third chapter focuses on three implementations of the GMM: the Two-Step algorithm, the Iterated algorithm, and the Continuously updating procedure. In the fourth chapter, the accuracy of the MM and the GMM estimates is investigated and the GMM implementa- tions are compared. 1
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Tests of statistical hypotheses in measurement error models
Navrátil, Radim ; Jurečková, Jana (advisor) ; Hušková, Marie (referee) ; Kalina, Jan (referee)
The behavior of rank procedures in measurement error models was studied - if tests and estimates stay valid and applicable when there are some measurement errors involved and if not how to modify these procedures to be able to do some statistical inference. A new rank test for the slope parameter in regression model based on minimum distance esti- mator and an aligned rank test for an intercept were proposed. The (asymptotic) bias of R-estimator in measurement error model was also investigated. Besides measurement errors the problem of heteroscedastic model errors was considered - regression rank score tests of heteroscedasticity with nuisance regression and tests of regression with nuisance heterosce- dasticity were proposed. Finally, in location model tests and estimates of shift parameter for various measurement errors were studied. All the results were derived theoretically and then demonstrated numerically with examples or simulations.
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Tests for Multiple Changes in Linear Regression Models
Marušiaková, Miriam ; Hušková, Marie (advisor) ; Prášková, Zuzana (referee) ; Picek, Jan (referee)
We consider tests for multiple structural changes in linear regression models. The tests are based on F-type test statistics for the null hypothesis of no change against k changes or against an unknown number of changes with a given upper bound. We extend the existing results to linear regression models with deterministically trending regressors. Moreover, we introduce a generalized M-type test statistic which is based on functionals of weighted M-residuals. In change-point analysis approximations to critical values are usually obtained through the limit behavior of the respective test statistic under the null hypothesis. However, these approximations are often not satisfactory. Either the convergence of the test statistic to its limit distribution is rather slow or the limit distribution itself is very complex. An alternative approach is to apply resampling methods. We explore this possibility for F-type and M-type test statistics in the presence of multiple change points. We prove that the bootstrap method provides asymptotically correct critical values for the studied tests. We conduct several simulation experiments to show that the bootstrap based approximations are reasonable also in nite sample situations. Moreover, these approximations are often better than the asymptotic critical values. Finally, we...
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