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Estimation of the Location of Zeros of Regression Functions
Juríček, Jozef ; Zvára, Karel (referee) ; Hlávka, Zdeněk (advisor)
The main interest of this master thesis is the estimation of location of zeros of the regression function and its derivatives by the parametric and nonparametric method. The first section includes either linear and nonlinear regression model of the parametric methods. The estimators are then based on the estimates of parameters. The second part includes nonparametric regression model - kernel estimators of the regression function and its derivatives investigated by Gasser and Müller. Especially, the limit distributions of the estimators of zeros and the choice of smoothing parameter and kernel function are studied. Confidence bands for zeros of regression function and its derivatives are constructed in both sections. Models are studied with independent as well as correlated errors. This master thesis o®ers examples to particular sections that are computed with software R and also sources of some programmed functions.
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Seeming regression of economic indices
Komzáková, Magdalena ; Zvára, Karel (referee) ; Lachout, Petr (advisor)
In the time series analysis it often appears that two or more time series influence each other. When the generating stochastic processes of these series do not have stationary structure but they are stochastically non-stationary, i.e. the characteristic polynomial has a unit root, it happens that the regression modelling the dependence of some absolutely independent series gives statistically significant parameter estimations and statistics used to judge the model fitting do not indicate anything about its impropriety. This phenomenon is called seeming regression (spurious regression) and is solved with the theory of cointegration. We can say that when the series are cointegrated, their model shows their real dependence, not only the seeming one. Due to this fact, cointegration tests are also used for testing for the presence of seeming regression. These tests are based on unit root tests in generating process (or on stationarity tests), because time series can be cointegrated only if their linear combination is a stationary series.
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