|
|
Detekce změn v lineárních modelech a bootstrap
Čellár, Matúš ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee)
This thesis discusses the changes in parameters of linear models and methods of their detection. It begins with a short introduction of the two basic types of change point detection procedures and bootstrap algorithms developed specifically to deal with dependent data. In the following chapter we focus on the location model - the simplest example of a linear model with a change in parameters. On this model we will illustrate a way of long-run variance estimation and implementation of selected bootstrap procedures. In the last chapter we show how to extend the applied methods to linear models with a change in parameters. We will compare the performance of change point tests based on asymptotic and bootstrap critical values through simulation studies in both our considered methods. The performance of selected long-run variance estimator will also be examined both for situations when the change in parameters occurs and when it does not. 1
|
|
|
Statistical inference in multivariate distributions based on copula models
Kika, Vojtěch ; Omelka, Marek (advisor) ; Hlubinka, Daniel (referee)
Diploma thesis abstract Thesis title: Statistical inference in multivariate distributions based on copula models Author: Vojtěch Kika This diploma thesis aims for statistical inference in copula based models. Ba- sics of copula theory are described, followed by methods for statistical inference. These are divided into three main groups. First of them are parametric methods for copula parameter estimation which assume fully parametric structure, thus for both joint and marginal distributions. The second group consists of semi- parametric methods for copula parameter estimation which, unlike parametric methods, do not require parametric structure for marginal distributions. The last group describes goodness-of-fit tests used for testing the hypothesis that consi- dered copula belongs to some specific copula family. The thesis is accompanied by a simulation study that investigates the dependence of the observed coverage of the asymptotic confidence intervals for copula parameter on the sample size. Pseudolikelihood method was chosen for the simulation study since it is one of the most popular semiparametric methods. It is shown that sample size of 50 seems to be sufficient for the observed coverage to be close to the theoretical one. For Frank and Gumbel-Hougaard copula families even sample size of 30 gives us...
|
|
|
Detekce změn v lineárních modelech a bootstrap
Čellár, Matúš ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee)
This thesis discusses the changes in parameters of linear models and methods of their detection. It begins with a short introduction of the two basic types of change point detection procedures and bootstrap algorithms developed specifically to deal with dependent data. In the following chapter we focus on the location model - the simplest example of a linear model with a change in parameters. On this model we will illustrate a way of long-run variance estimation and implementation of selected bootstrap procedures. In the last chapter we show how to extend the applied methods to linear models with a change in parameters. We will compare the performance of change point tests based on asymptotic and bootstrap critical values through simulation studies in both our considered methods. The performance of selected long-run variance estimator will also be examined both for situations when the change in parameters occurs and when it does not. 1
|
|
|
Ověřování předpokladů modelu proporcionálního rizika
Marčiny, Jakub ; Kulich, Michal (advisor) ; Zvára, Karel (referee)
The Cox proportional hazards model is a standard tool for modelling the effect of covariates on time to event in the presence of censoring. The appropriateness of this model is conditioned by the validity of the proportional hazards assumption. The assumption is explained in the thesis and methods for its testing are described in detail. The tests are implemented in R, including self-written version of the Lin- Zhang-Davidian test. Their application is illustrated on medical data. The ability of the tests to reveal the violation of the proportional hazards assumption is investigated in a simulation study. The results suggest that the highest power is attained by the newly implemented Lin-Zhang-Davidian test in most cases. In contrast, the weighted version of the Lin-Wei-Ying test was found to have inadequate size for low sample sizes.
|
|
|
ASSET DIVIDING APPRASIAL MODEL (ADAM) - Hodnocení investic při přímém vkládání kapitálu do nemovitostí
Schäfer, Carsten ; Krabec, Tomáš (advisor) ; Hnilica, Jiří (referee) ; Starý, Oldřich (referee) ; Bernet, Jürg (referee)
The Asset Dividing Appraisal Model (ADAM) enables the appraisal of cash flows resulting from direct real estate investments. The model is an evaluation tool, which takes capital markets and the specific characteristics of real estate as an asset (heterogeneity, site-dependency, eternal land-yield, etc.) into consideration, while also considering different ownership approaches of real estate in the European Union. Thus, it contributes to the harmonization of capital markets and of direct real estate investment evaluation as intended by the "European Directive on Markets in Financial Instruments 2004/39/EC". ADAM is based on financial mathematical instruments and on the property valuation methods of different cultural areas. It combines continental European (Germ an Gross Rental-Method) and international (Discounted Cash Flow-Method) property valuation approaches. Although it is scientifically reasonable to take property valuation approaches into account, the aim of the model is not to valuate a property or to quantify an objective market value but to evaluate cash-flows resulting from direct real estate investments. A mathematical analysis based on empirical market data confirmed the validity of the methodology of the model. In the course of the analysis the major input variables that determine the results of the model and how the model reacts to marginal deviations of input data, were quantified. This was done using partial derivations and a simulation study. In Czech Republic a building isn't actually considered as a part of the underlying plot. Consequently, differing persons or institutions can be owner of the building, as of the appropriate plot. From 2014 on, a suitable reformation of the Czech Civil Code is supposed to cause a consolidation of real estate property. Czech law is going to be adjusted to German law, which considers plot and building as an economic entity. This consolidation of real estate could be an approach of the introduced model.
|
guest ::
