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Robust linear regression
Rábek, Július ; Maciak, Matúš (advisor) ; Nagy, Stanislav (referee)
Regression analysis is one of the most extensively used statistical tools applied across different fields of science, with linear regression being its most well-known method. How- ever, the traditional procedure to obtain the linear model estimates, the least squares approach, is highly sensitive to even slight departures from the assumed modelling frame- work. This is especially pronounced when atypical values occur in the observed data. This lack of stability of the least squares approach is a serious problem in applications. Thus, the focus of this thesis lies in assessing the available robust alternatives to least squares estimation, which are not so easily affected by any outlying values. First, we introduce the linear regression model theory and derive the least squares method. Then, we char- acterise different types of unusual observations and outline some fundamental robustness measures. Next, we define and examine the robust alternatives to the classical estimation in the linear regression models. Finally, we conduct a comprehensive simulation study comparing the performance of robust methods under different scenarios. 1
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Seasonal exponential smoothing
Rábek, Július ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This thesis deals with the issues of time series modeling, where seasonal component is present. Principles of basic seasonal exponential smoothing methods: simple and double exponential smoothing, Holt's method, which are applicable on time series without seasonality, are described in the beginning. For seasonal time series, Holt-Winters exponential smoothing is the most suitable method. This method is introduced in both of its versions and the usage of either version depends on the characteristics of the seasonal component. Furthermore, state space modeling is presented as a statistical framework for exponential smoothing methods, joined with a discussion of some selected problems related with practical implementation of these techniques together with suggestions of their solution. Finally, Holt-Winters method on two real data time series with seasonality is presented.
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