|
| |
|
| |
|
|
Models of changes in econometric time sequences
Strejc, Petr ; Hušková, Marie (advisor) ; Dvořák, Marek (referee)
This paper is concerned with change-point detection in parameters of econometric regression models when a training set of data without any change is available. There are presented two well- known sequential tests - CUSUM test for linear regression model and a test based on weighted residuals for an autoregressive time series - including their asymptotical properties under certain conditions. Two asymptotically equivalent variance estimators are compared in a finite sample situation using Monte Carlo simulations. There are also presented and compared critical value approximations using different bootstrapping methods and variance estimators. Finally, the weighted residual test is applied on S&P 500 historical data.
|
|
|
The U-statistics
Novák, Petr ; Madurkayová, Barbora (advisor) ; Hušková, Marie (referee)
Nazcv pracc: U-statistiky Autor: IVtr N'ovak Katcdra: Katedra, pravdepodobnosti a matematicke statistiky Vedouci bakalafske pracc: Mgr. Barbora Madurkayova c-tnail vedouciho: niadurkai''i~ikai-liii.inir.cuni.c'/ Abstrakt: V teto praci se budeine zabyvat vehni vyznamnou tfidou sta- tistik, U-statistikami. Tyto json zobecnenim vyberoveho prumeru, vybcro- veho rozptylu i dalsich zuainych statistik. V praci sc nejprve scznamnjeme s prolilciny, ktcrr vcdly k objcvu U-statistik, a jejic:h frsenim. Pf> zavcclcni U-statistik ye soznaniiiiK1 s nektcrynii jcjich vlastno.stini, diky ktcryin json /.name. Dale so bndenic zabyvat jejich ro/]jtyloin a jcho vhodnyin vyjadfe- nini a take kovarianci dvon rnznych U-statistik. Pote odvodiine take odhady pro vyssi momenty U-statistik, ktero pro vrtsiim vypoctu i>ostac\\ji. V dalsi kapitole st! take zniiniiiH1 o II-rozkladn U-statistik. Na '/aver se zamerhne na, spojitost U-statistik y inartiiigaly. Klicova slova: U-statistiky, II-rozklad, Martingal Title: U-statistics Author: Petr .\ov;ik Department: De])a,rtineiit of Probability and Mathematical Statistics Supervisor: Mgr. Barbora Madurkayova Supervisor's c-niail address: madnrka«"karlin.infrcnni.cz Abstract: In this work we consider important class of statistics, U-Statistics. These arc generalisation of .sample mean, sample...
|
|
| |
|
|
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 methods for interpreting forensic DNA mixtures
Kubátová, Helena ; Zvárová, Jana (advisor) ; Hušková, Marie (referee)
In the present work we study interpretation of forensic DNA evidence from the point of view of probability theory and mathematical statistics. We provide a detailed mathematical formalization of the problem, which enables us to formulate mathematically accurate and consistent results. We deal with evaluation of a given evidence in terms of a likelihood ratio, which compares two hypotheses speci ed by genotypes of known contributors and the number of unknown contributors to the DNA mixture. We further analyze the case of a subdivided population, performing a thorough revision of the formulas for homozygous and heterozygous genotypes, their general version and a theorem for calculating the probability that an assumed number of random individuals explain a given genetic evidence.
|
|
| |
guest ::
RSS feed.