National Repository of Grey Literature 98 records found  1 - 10nextend  jump to record: Search took 0.00 seconds. 
Confidence regions in nonlinear regression
Marcinko, Tomáš ; Zvára, Karel (advisor) ; Komárek, Arnošt (referee)
The aim of this thesis is a comprehensive description of the properties of a nonlinear least squares estimator for a nonlinear regression model with normally distributed errors and thorough development of various methods for constructing confidence regions and confidence intervals for the parameters of the nonlinear model. Due to the fact that, unlike the case of linear models, there is no easy way to construct an exact confidence region for the parameters, most of these methods are only approximate. A short simulation study comparing observed coverage of various confidence regions and confidence intervals for models with different curvatures and sample sizes is also included. In case of negligible intrinsic curvature the use of likelihood-ratio confidence regions seems the most appropriate.
Multicollinearity
Dřizgová, Lucie ; Zvára, Karel (advisor) ; Hlávka, Zdeněk (referee)
In our work, we explored multicollinearity problem from a complex point of view - from diagnostic methods to the solving of the problems which are caused by the multicollinearity. We compared the Least Squares method with some alternative methods - Principal Component Regression, Partial Least Squares Regression and Ridge Regression on the theoretical basis. In the last section, we demonstrated all methods on practical example computed in the program R.
Mathematical Models for LGD
Rychnovský, Michal ; Charamza, Pavel (advisor) ; Zvára, Karel (referee)
The aim of the present work is to describe possible models for LGD estimation and to test them on the real data. Besides common linear and logistic regression models we aim to describe the methods using running and censored observations - based on the Cox model and the two-step regression. This work first briefly outlines the principle of the capital requirement according to the Basel II. Then, individual methods are described and finally applied to the real banking data.
Asymptotic properties of the weighted least squares estimate
Gajdošík, Vladislav ; Víšek, Jan Ámos (advisor) ; Zvára, Karel (referee)
This diploma thesis dissertate about consistency and asymptotic representation of the least weighted squares estimator (LWS). In preface we mention reasons for data processing with robust statistical methods and differencies between LWS estimator and other methods (the least squares estimator, the least trimmed squares estimator). In the following sections we show proofs of lemmas about consistency and assymptotic representation of the least weighted squares estimator. Compared to the similar results published before we have concluded ours based on different conditions. Impulse for this thesis were new results about uniform convergence of empirical function mentioned in work from prof. Jan Ámos Víšek - Kolmogorov-Smirnov statistics in multiple regression from year 2006 (see Víšek (2006a)).
Regression trees
Masaila, Aleh ; Hanzák, Tomáš (advisor) ; Zvára, Karel (referee)
Title: Regression trees Author: Aleh Masaila Department: Department of Probability and Mathematical Statistics Supervisor: Mgr.Tomáš Hanzák Abstract: Although regression and classification trees are used for data analysis for several decades, they are still in the shadow of more traditional methods such as linear or logistic regression. This paper aims to describe a couple of the most famous regression trees and introduce a new direction in this area - a combination of regression trees and committee methods, so called the regression forests. There is a practical part of work where we try properties, strengths and weaknesses of the examined methods on real data sets. Keywords: regression tree, CART, MARS, regression forest, bagging, boosting, random forest 1
Nonlinearity in time series models
Kalibán, František ; Anděl, Jiří (advisor) ; Zvára, Karel (referee)
The thesis concentrates on property of linearity in time series models, its definitions and possibilities of testing. Presented tests focus mainly on the time domain; these are based on various statistical methods such as regression, neural networks and random fields. Their implementation in R software is described. Advantages and disadvantages for tests, which are implemented in more than one package, are discussed. Second topic of the thesis is additivity in nonlinear models. The definition is introduced as well as tests developed for testing its presence. Several test (both linearity and additivity) have been implemented in R for purposes of simulations. The last chapter deals with application of tests to real data. 1
Regression models with alternatively distributed response
Kučera, Tomáš ; Komárek, Arnošt (advisor) ; Zvára, Karel (referee)
This thesis deals with regression models in the case of binary response variable. Linear and logistic regression models are defined for different types of predictors. Then the thesis uses the theory of maximum likelihood and applies it to the special case of logistic regression model. Both exact inference of model parameters and hypothesis testing with related interval inference are discussed. Suitable methods for numerical solving of selected methods are suggested. In the final part, the discussed methods are applied to real credit scoring data from the field of banking, using the statistical software R.

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