Odborné statistické materiály

Estimation and goodness-of-fit criteria in logistic regression model, Bachelor thesis, MFF UK. In this bachelor thesis is described binary logistic regression model and estimation of model's parameters by maximum likelihood method. Then there is proposed algorithm for the least squares method. In the goodness-of-fit criteria part is defined Lorenz curve, Gini coefficient, C-statistics, Kolmogorov-Smirnov statistics and coefficient of determination R2. Their relation to different sample coefficients of correlation is derived. Typical relation between Gini coefficient, Kolmogorov-Smirnov statistics is derived and newly also coefficient of determination R2 via model of normally distributed score of bad and good clients. These derived theoretical results are verified on three real data sets.

Statistical error in representative samples from population, Bachelor thesis, MFF UK.This thesis deals with statistical error estimation in sampling surveys. The aim was to find corrections of statistical error estimations in the situations where the data are weighted or where the data originate from quota samples. It is shown using theoretical considerations to derive more accurate statistical error estimation in the case of quota sample with one quota variable. Test of the validity of adjusted estimate using simulations is shown in the case of weighed data we. Application and comparison of three different methods is demonstrated on the real poll model data and construction of empirical error estimates.

Derivatives pricing using Monte Carlo simulations, Diploma thesis, University of Economics.This present work focuses on methods of variance reduction of estimations generated by Monte Carlo simulation and their application. Theoretical part of this work contains description of six methods mentioned in current literature. These methods are applied to the valuation of one type of barrier option, so called up-and-out option. First, work focuses on widely used model of underlying asset price process, diffusion process with constant parameters (also called geometric Brownian motion). Then model with stochastic volatility is applied. Then methods of variance reduction are applied and discussed.

Exponential Smoothing for Irregular Time Series. Kybernetika magazine. The paper deals with extensions of exponential smoothing methods for univariate irregular time series. An alternative method to Wright’s modification of simple exponential smoothing is suggested. Exponential smoothing of order m for irregular data is derived in two different ways. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.

Improved Holt method for irregular time series. WDS´08 Proceedings of Contributed Papers, Part I, 2008. The paper suggests an improvement of Holt method for irregular time series as it was presented by Wright. The modification deals with problem of time-close observations. Simulation study is provided to compare the performance of the original and improved method.

Irregular Periodic Time Series. Dissertation progress report, speech on a doctoral seminar Stochastic modelling in economics and finance, MFF UK.

Exponential Smoothing, Bachelor thesis, MFF UK. The thesis deals with two exponential smoothing type methods for non-seasonal time series with local linear trend. The main part of the thesis is a theoretical derivation of MSE and autocorrelation coefficient of forecasting errors when using Holt method with all combinations of smoothing constants and with the time series generated by ARIMA(0, 2, 2) process with all combinations of its parameters. theoretically derived formulae are applied also to Brown method, derived formulae are verified via simulations and tried on real time series. The practical conclusions related to both methods are formulated.

Exponential Smoothing for Irregular Time Series. Poster for Robust 2008 conference. In this poster are highlighted problems resulting from irregularity of observations and suggested possible solutions. Beside already published methods are presented methods or their modifications by author ( m ranked exponential smoothing, irregularly observed ARIMA(0, 1, 1) process, modified Holt’s method, Holt-Winters method modeling seasonality by goniometric functions).

Cointegrated Time Series Models, Diploma thesis, MFF UK. The thesis deals with the concept of cointegration which represents appropriate tool in the analysis of nonstationary processes. Thesis concentrates on the models which are commonly used in the cointegration analysis of the time series. It describes straight connection between error-correction (EC) model and autoregressive distributed lags model (ADL). Theoretical results are applied on real data in demand for money model.

Weak convergence in D[0,1]. Presentation for PhD. seminar Stochastic modeling in economics and finance, MFF UK, 2008. Presentation topic is weak convergence in space D[0,1].

Geometrical Properties of the r - neighborhood of Brownian Motion and Related Random Structures. Doctoral dissertation, MFF UK. The thesis is mainly focused on the study of a particular random compact set called Wiener sausage. Heuristically, it is the trace of a moving spherical object in Euclidean space along Brownian trajectories up to finite time. Apart from expected volume and surface area also their assymptotical behaviour is studied. Moreover, main characteristics of Boolean model of Wiener sausages are derived.

Decomposition Methods for Time Series with Irregular Observations, Diploma thesis MFF UK. This work deals with extensions of classical exponential smoothing type methods for univariate time series with irregular observations. Extensions of simple exponential smoothing, Holt method, Holt-Winters method and double exponential smoothing which have been developed in past are presented. An alternative method to Wright's modification of simple exponential smoothing for irregular data. A program in which most of the methods presented here are available is a part of the work.

Problem of estimation annual average concentration of radon in building. Seminar work on subject Econometrics, MFF UK. Aim of this work is to construct estimation of annual average concentration of radon in building based on shorter observations. Available were real data from the state office for radiation protection (concentration of radon in observed building and basic meteorological data).

Summary of statistical errors in survey sampling estimation methods. Published in yearbook Statistika ČSÚ, 2005. In this article several possible procedures appropriate for estimation of statistical error in case of relative frequencies are studied. It focuses on different types of suitable probability distributions (hypergeometric, binomial, Poisson) including possible approximations (normal distribution). It suggests also alternative methods for error estimation (bootstrap and jacknife) and methods for error estimation in case of cluster sampling . The present work also deals with error estimation of other commonly used characteristics as averages and standard deviations.

Gibbsian Processes of Convex Grains. Paper at Week of doctoral studies. Gibbsian processes of grains are usually constructed as marked point processes with grains situated in its points, where the distribution of grains is deterministic or comes from some family of distributions. We construct Gibbs model directly from the definition of a pair potential defined on pairs of bounded sets in Rd.