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Modification of Regression Function
Popoola, Seyi James ; Hübnerová, Zuzana (oponent) ; Žák, Libor (vedoucí práce)
The regression analysis is a modelling technique that establishes, mathematically, the relationship between entities of a particular subject. Although the modelling is done in such a way that one variable is seen as a subject of the other(s), regression does not imply causation. The modeling has assumptions such as linearity, normality, little or no multicollinearity, homoscedasticity as conditions for optimal relationship establishment. The simplest of the regression technique is the linear regression which also is the most commonly used. It involves the use of a straight line model to define the best pattern of relationship. This best pattern is assessed by the measure of goodness of fit which describes the amount of variation in the response variable explained by the stimuli (or stimulus). Change-point regression is a type of linear regression that takes into account a change in course of the movement of the relationship under study. This type of change in course is taken into account by modelling the regression in segments to account for the entire relationship observable in the data at hand. Several information criterions are used for detecting this change in course, the Schwartz Information Criterion (SIC), the Bayesian Information Criterion (BIC), amongst others. The detection method adopted for this work is the Modified Information Criterion (MIC) which tests a null hypothesis of no change point against an alternative that states presence of change-point. The data upon which this methodology is applied is the Italy COVID-19 data. The data was subjected to a linear regression and evaluated after which it was subjected to this change point test and the test shows the presence of a change in course. The sections which the test divides the data into were modelled individually and their regression lines were obtained. The two sections were plotted on a graph with their regression lines intercepting at the crest of the plot.
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Boundary effects in signal processing: From classical problems to new opportunities
Popoola, Seyi James ; Druckmüllerová, Hana (oponent) ; Cicone, Antonio (vedoucí práce)
This thesis focuses on boundary issues in the decomposition of signals. Classical methods boundary issues have been studied extensively, but a new generation of methods has been introduced in the last couple of decades. The implementation of these novel methods has the potential to produce in an efficient way more accurate, flexible, and interpretable results, which can help advance research in real-life applications in various fields. Boundary issues for these techniques have been studied only recently. The results published so far shows that these methods have limitations and assumptions that need to be carefully considered to avoid potential misuse. In this study, we pinpoint and tackle the major obstacles associated with the use these new methods, and the recommendations on how to utilize them most effectively is also provided. To further illustrate the potential consequences of improper usage, we undertake a comprehensive examination of their application to actual data and carry out numerical simulations. Lastly, we propose a set of best practices for optimizing the performance of these techniques in the context of signal decomposition. A crucial suggestion is to employ, before applying any decomposition method, a signal extension technique as a means of mitigating boundary effects.
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Modification of Regression Function
Popoola, Seyi James ; Hübnerová, Zuzana (oponent) ; Žák, Libor (vedoucí práce)
The regression analysis is a modelling technique that establishes, mathematically, the relationship between entities of a particular subject. Although the modelling is done in such a way that one variable is seen as a subject of the other(s), regression does not imply causation. The modeling has assumptions such as linearity, normality, little or no multicollinearity, homoscedasticity as conditions for optimal relationship establishment. The simplest of the regression technique is the linear regression which also is the most commonly used. It involves the use of a straight line model to define the best pattern of relationship. This best pattern is assessed by the measure of goodness of fit which describes the amount of variation in the response variable explained by the stimuli (or stimulus). Change-point regression is a type of linear regression that takes into account a change in course of the movement of the relationship under study. This type of change in course is taken into account by modelling the regression in segments to account for the entire relationship observable in the data at hand. Several information criterions are used for detecting this change in course, the Schwartz Information Criterion (SIC), the Bayesian Information Criterion (BIC), amongst others. The detection method adopted for this work is the Modified Information Criterion (MIC) which tests a null hypothesis of no change point against an alternative that states presence of change-point. The data upon which this methodology is applied is the Italy COVID-19 data. The data was subjected to a linear regression and evaluated after which it was subjected to this change point test and the test shows the presence of a change in course. The sections which the test divides the data into were modelled individually and their regression lines were obtained. The two sections were plotted on a graph with their regression lines intercepting at the crest of the plot.
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