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Analysis of spectral characteristics of signals
Sedláček, Matyáš ; Klejmová, Eva (referee) ; Poměnková, Jitka (advisor)
The subject of this bachelor’s thesis are the properties of power spectral density estimates, mainly how their properties depend on the analyzed signal’s parameters and the method being used. Important signal properties from the perspective of spectral analysis are defined, as well as measures for judging the estimate. Based on those, a choice of nonparametric and parametric spectral estimation methods is described. Analysis is performed on simulated signals and the results generalized into a set of recommendations for finding an estimate via an optimal method. These recommendations are then scrutinized and further discussed through estimation of real signal PSDs. Included is an application in MATLAB App Designer for generating spectral estimates and a collection of signals used.
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Analysis of spectral characteristics of signals
Sedláček, Matyáš ; Klejmová, Eva (referee) ; Poměnková, Jitka (advisor)
The subject of this bachelor’s thesis are the properties of power spectral density estimates, mainly how their properties depend on the analyzed signal’s parameters and the method being used. Important signal properties from the perspective of spectral analysis are defined, as well as measures for judging the estimate. Based on those, a choice of nonparametric and parametric spectral estimation methods is described. Analysis is performed on simulated signals and the results generalized into a set of recommendations for finding an estimate via an optimal method. These recommendations are then scrutinized and further discussed through estimation of real signal PSDs. Included is an application in MATLAB App Designer for generating spectral estimates and a collection of signals used.
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Weighted Data Depth and Depth Based Discrimination
Vencálek, Ondřej ; Hlubinka, Daniel (advisor) ; Anděl, Jiří (referee) ; Malý, Marek (referee)
The concept of data depth provides a powerful nonparametric tool for multivariate data analysis. We propose a generalization of the well-known halfspace depth called weighted data depth. The weighted data depth is not affine invariant in general, but it has some useful properties as possible nonconvex central areas. We further discuss application of data depth methodology to solve discrimination problem. Several classifiers based on data depth are reviewed and one new classifier is proposed. The new classifier is a modification of k-nearest- neighbour classifier. Classifiers are compared in a short simulation study. Advantage gained from use of the weighted data depth for discrimination purposes is shown.
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Weighted Halfspace Depths and Their Properties
Kotík, Lukáš
Statistical depth functions became well known nonparametric tool of multivariate data analyses. The most known depth functions include the halfspace depth. Although the halfspace depth has many desirable properties, some of its properties may lead to biased and misleading results especially when data are not elliptically symmetric. The thesis introduces 2 new classes of the depth functions. Both classes generalize the halfspace depth. They keep some of its properties and since they more respect the geometric structure of data they usually lead to better results when we deal with non-elliptically symmetric, multimodal or mixed distributions. The idea presented in the thesis is based on replacing the indicator of a halfspace by more general weight function. This provides us with a continuum, especially if conic-section weight functions are used, between a local view of data (e.g. kernel density estimate) and a global view of data as is e.g. provided by the halfspace depth. The rate of localization is determined by the choice of the weight functions and theirs parameters. Properties including the uniform strong consistency of the proposed depth functions are proved in the thesis. Limit distribution is also discussed together with some other data depth related topics (regression depth, functional data depth)...
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Weighted Halfspace Depths and Their Properties
Kotík, Lukáš
Statistical depth functions became well known nonparametric tool of multivariate data analyses. The most known depth functions include the halfspace depth. Although the halfspace depth has many desirable properties, some of its properties may lead to biased and misleading results especially when data are not elliptically symmetric. The thesis introduces 2 new classes of the depth functions. Both classes generalize the halfspace depth. They keep some of its properties and since they more respect the geometric structure of data they usually lead to better results when we deal with non-elliptically symmetric, multimodal or mixed distributions. The idea presented in the thesis is based on replacing the indicator of a halfspace by more general weight function. This provides us with a continuum, especially if conic-section weight functions are used, between a local view of data (e.g. kernel density estimate) and a global view of data as is e.g. provided by the halfspace depth. The rate of localization is determined by the choice of the weight functions and theirs parameters. Properties including the uniform strong consistency of the proposed depth functions are proved in the thesis. Limit distribution is also discussed together with some other data depth related topics (regression depth, functional data depth)...
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Weighted Halfspace Depths and Their Properties
Kotík, Lukáš ; Hlubinka, Daniel (advisor) ; Omelka, Marek (referee) ; Mosler, Karl (referee)
Statistical depth functions became well known nonparametric tool of multivariate data analyses. The most known depth functions include the halfspace depth. Although the halfspace depth has many desirable properties, some of its properties may lead to biased and misleading results especially when data are not elliptically symmetric. The thesis introduces 2 new classes of the depth functions. Both classes generalize the halfspace depth. They keep some of its properties and since they more respect the geometric structure of data they usually lead to better results when we deal with non-elliptically symmetric, multimodal or mixed distributions. The idea presented in the thesis is based on replacing the indicator of a halfspace by more general weight function. This provides us with a continuum, especially if conic-section weight functions are used, between a local view of data (e.g. kernel density estimate) and a global view of data as is e.g. provided by the halfspace depth. The rate of localization is determined by the choice of the weight functions and theirs parameters. Properties including the uniform strong consistency of the proposed depth functions are proved in the thesis. Limit distribution is also discussed together with some other data depth related topics (regression depth, functional data depth)...
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Weighted Data Depth and Depth Based Discrimination
Vencálek, Ondřej ; Hlubinka, Daniel (advisor) ; Anděl, Jiří (referee) ; Malý, Marek (referee)
The concept of data depth provides a powerful nonparametric tool for multivariate data analysis. We propose a generalization of the well-known halfspace depth called weighted data depth. The weighted data depth is not affine invariant in general, but it has some useful properties as possible nonconvex central areas. We further discuss application of data depth methodology to solve discrimination problem. Several classifiers based on data depth are reviewed and one new classifier is proposed. The new classifier is a modification of k-nearest- neighbour classifier. Classifiers are compared in a short simulation study. Advantage gained from use of the weighted data depth for discrimination purposes is shown.
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Statistical Evaluation of Atmospheric Mercury Measurements Conducted in Parallel with Two Identical Instruments
Veselík, P. ; Dvorská, Alice ; Michálek, J.
At the Atmospheric Station Křešín u Pacova, central Czech Republic, total gaseous mercury was measured in background ambient air with two automatic mercury TEKRAN 2537B analyzers positioned right next to each other in one container. The measurements were conducted with a 10 min time step, between December 2012 and August 2013. The aim of the study was to confirm or exclude the hypothesis of same measurement results provided by the instruments. Measured data were aggregated into 1 week subsets and statistically analysed. The data was graphically visualised and evaluated by using exploratory data analysis. For comparing the performance of both instruments nonparametric statistical analysis (Wilcoxon matched pairs test) was used. The performed analysis shows statistically significant differences between measurements from the two instruments.
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