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Logistic regression with applications in financial sector
Bílková, Kristýna ; Branda, Martin (advisor) ; Pešta, Michal (referee)
In this bachelor thesis binary logistic regression model is described. Its parameters are estimated by maximum likelihood method. Newton-Raphson's algorithm is used for enumeration of these estimates. There are defined some statistics for testing the significance of the coefficients. Then stepwise regression is desribed. For assessing the quality of the model Pearson's Chi Square Test and Hosmer-Lemeshow's Test of the goodness of fit are defined. Diversification abilitz of the model is illustrated bz the Loreny curve and is quantificated by Gini coefficient, Kolmogorov-Smirnov statistics and generalized coefficient of determination. The theoretical knowledge is applied to insurance area data.
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Tests in multinomial distribution
Holý, Vladimír ; Anděl, Jiří (advisor) ; Antoch, Jaromír (referee)
In this paper there are at first described classical goodness-of-fit tests - the Pear- son's χ2 test and the log likehood ratio test. The more modern method of testing is the family of statistics based on power divergence which is generalisation of classical statistics. Another type of generalisation is the family of disparity statis- tics which includes beside the family of power divergence also the families BWHD and BWCS. It is demonstrated that all these test statistics have an asymptotic χ2 distribution. In the program R the exact level and exact power can be calculated for individual tests. Hereafter, moments of test statistics can be derived. On the basis of these comparisons there will be shown which test statistics are the most suitable for the goodness-of-fit tests. 1
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Statistical inference in multivariate distributions based on copula models
Kika, Vojtěch ; Omelka, Marek (advisor) ; Hlubinka, Daniel (referee)
Diploma thesis abstract Thesis title: Statistical inference in multivariate distributions based on copula models Author: Vojtěch Kika This diploma thesis aims for statistical inference in copula based models. Ba- sics of copula theory are described, followed by methods for statistical inference. These are divided into three main groups. First of them are parametric methods for copula parameter estimation which assume fully parametric structure, thus for both joint and marginal distributions. The second group consists of semi- parametric methods for copula parameter estimation which, unlike parametric methods, do not require parametric structure for marginal distributions. The last group describes goodness-of-fit tests used for testing the hypothesis that consi- dered copula belongs to some specific copula family. The thesis is accompanied by a simulation study that investigates the dependence of the observed coverage of the asymptotic confidence intervals for copula parameter on the sample size. Pseudolikelihood method was chosen for the simulation study since it is one of the most popular semiparametric methods. It is shown that sample size of 50 seems to be sufficient for the observed coverage to be close to the theoretical one. For Frank and Gumbel-Hougaard copula families even sample size of 30 gives us...
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Goodness of fit tests with nuisance parameters
Baňasová, Barbora ; Hušková, Marie (advisor) ; Hlávka, Zdeněk (referee)
This thesis deals with the goodness of fit tests in nonparametric model in the presence of unknown parameters of the probability distribution. The first part is devoted to understanding of the theoretical basis. We compare two methodologies for the construction of test statistics with application of empirical characteristic and empirical distribution functions. We use kernel estimates of regression functions and parametric bootstrap method to approximate the critical values of the tests. In the second part of the thesis, the work is complemented with the simulation study for different choices of weighting functions and parameters. Finally we illustrate the use and the comparison of goodness of fit tests on the example with the real data set. Powered by TCPDF (www.tcpdf.org)
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Logistic regression with applications in financial sector
Bílková, Kristýna ; Branda, Martin (advisor) ; Pešta, Michal (referee)
In this bachelor thesis binary logistic regression model is described. Its parameters are estimated by maximum likelihood method. Newton-Raphson's algorithm is used for enumeration of these estimates. There are defined some statistics for testing the significance of the coefficients. Then stepwise regression is desribed. For assessing the quality of the model Pearson's Chi Square Test and Hosmer-Lemeshow's Test of the goodness of fit are defined. Diversification abilitz of the model is illustrated bz the Loreny curve and is quantificated by Gini coefficient, Kolmogorov-Smirnov statistics and generalized coefficient of determination. The theoretical knowledge is applied to insurance area data.
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Tests in multinomial distribution
Holý, Vladimír ; Anděl, Jiří (advisor) ; Antoch, Jaromír (referee)
In this paper there are at first described classical goodness-of-fit tests - the Pear- son's χ2 test and the log likehood ratio test. The more modern method of testing is the family of statistics based on power divergence which is generalisation of classical statistics. Another type of generalisation is the family of disparity statis- tics which includes beside the family of power divergence also the families BWHD and BWCS. It is demonstrated that all these test statistics have an asymptotic χ2 distribution. In the program R the exact level and exact power can be calculated for individual tests. Hereafter, moments of test statistics can be derived. On the basis of these comparisons there will be shown which test statistics are the most suitable for the goodness-of-fit tests. 1
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