|
|
Expectile regression
Ondřej, Josef ; Komárek, Arnošt (advisor) ; Pešta, Michal (referee)
In this thesis we present an alternative to quantiles, which is known as expectiles. At first we define the notion of expectile of a distribution of ran- dom variable and then we show some of its basic properties such as linearity or monotonic behavior of τ-th expectile eτ in τ. Let (Y, X), Y ∈ R, X ∈ Rp be a ran- dom vector. We define conditional expectile of Y given X = x, which we denote eτ (Y |X = x). We introduce model of expectile regression eτ (Y |X = x) = x⊤ βτ , where βτ ∈ Rp and we examine asymptotic behavior of estimate of the regression coefficients βτ and ways how to calculate it. Further we introduce semiparametric expectile regression, which generalizes the previous case and adds restrictions on the estimate of the regression coefficients which enforce desired properties such as smoothness of fitted curves. We illustrate the use of theoretical results on me- chanographic data, which describe dependence of power and force of a jump on age of children and adolescents aged between 6 and 18. Keywords: expectiles, expectile regression, quantiles, penalized B-splines 1
|
|
| |
|
|
EM algorithm
Vacula, Ondřej ; Komárek, Arnošt (advisor) ; Antoch, Jaromír (referee)
This paper discusses the EM algorithm. This algorithm is used, for example, to calculate maximum likelihood estimate of unknown parameter. The algorithm is based on repeated calculations of certain expected value and maximizing specific function. We begin with parameter estimation problem, describe the maximum likelihood method and concept of incomplete data. Then we formulate the EM algorithm and its properties. In the next chapter we apply this knowledge to three selected statistical problems. At first we examine standard mixture model, then the linear mixed model and finally we analyze censored data. Powered by TCPDF (www.tcpdf.org)
|
|
|
Simultaneous confidence intervals dual to stepwise methods of multiple comparison
Moravec, Jan ; Komárek, Arnošt (advisor) ; Hlávka, Zdeněk (referee)
The central theme of this thesis is the construction of simultaneous confidence regions (SCR) corresponding to stepwise multiple comparison procedures (MCP). The first chapter is devoted to the theory of multiple comparisons, including the class of closed testing procedures which contains every MCP that strongly con- trols the familywise error rate. The second chapter is concerned with the gene- ral principle of construction of SCR corresponding to closed testing procedures. These general results are used in the third and the forth chapter for deriving the SCR corresponding to a subclass of closed testing procedures which are based on weighted Bonferroni tests. The SCR corresponding to the Holm, the Holm(W), the fixed-sequence and the fallback MCP are derived explicitly. The theoretical results are numerically illustrated on a bioequivalence study. In the fifth chapter we briefly discuss the SCR corresponding to the Hommel, the Hochberg and the step-down Dunnett MCP.
|
|
| |
|
|
Some problems of exponential smoothing
Čurda, David ; Hanzák, Tomáš (advisor) ; Komárek, Arnošt (referee)
In this work the several exponential smoothing type methods are briefly described, which are often used to smoothing and forecasting in the time series. Selected problems, that occur in described methods, are presented and in some cases there are the suggestions to their solution, which should tend to more suitable smoothing or to the better forecasts. It's shown how the methods are applied on different data and how the forecasts differ from each other. In conclusion the quality of modifications is evaluated.
|
|
|
Regression analysis and splines
Benko, Milan ; Bašta, Milan (advisor) ; Komárek, Arnošt (referee)
The aim of this Bachelor's thesis is to introduce the basic concepts of regression analysis and subsequently regression splines as parametric models for regression function. I have looked upon the main characteristics of regression splines (coherence, coherence of derivations, the choice of placement and a number of knots). Further on in the thesis I have studied two bases as the examples of regression splines (truncated power basis and B-spline basis). I have also presented a model of natural cubic splines and a suitable basis for its representation has been derived. In the other part of my thesis I have looked upon the use of natural splines in order to increases the appraisal precision of regression function, mean square error formula has been derived and I have been trying to find out and illustrate under what conditions the use of natural splines is applicable. The thesis is complemented with a Monte Carlo Simulation, contextualized into models of splines. The results show that the criteria commonly used for the choice of a model ($\R_{adj}^2$, $PRESS$ statistic, hypothesis testing) do not always enable us to choose the right model in order to achieve the greatest precision of the estimation of regression function. All the calculations are done in R software and are in the electronic attachment....
|
|
| |
|
|
Limited and censored explained variables
Kostka, Rudolf ; Bejda, Přemysl (advisor) ; Komárek, Arnošt (referee)
In this thesis at first we focus on theory of dealing with limited and censored explained variables. We begin with discrete variables and show the theory of binary and categorical variables. Later we explain utility of models logit and probit and demonstrate it at a practical example. We also provide a comparison of these two models. Third chapter deals with limited explained variables, specifically censored, truncated and variables representing some time to event. In the last chapter we describe some functions, which might be used to plot a graph of a survival function using softwares R or Mathematica. Some options in Excel are also mentioned, but they are very limited. Described functions are then demonstrated in use at a practical example with our gained data. Powered by TCPDF (www.tcpdf.org)
|
|
| |
guest ::
