The subject matter of this master thesis is the introduction to the claims reserving methodology applied in the general insurance with the focus on the agragated data represented in the form of triangle schemes. First the basic deterministic methods are to be presented including the Chain ladder method as the most known and widely used tool in claims reserving. Next we will concentrate on the stochastic approaches. The method of bootstrapping is to be described more in detail as it is the main topic of this thesis. Finally the accuracy of the prediction of several specific models and algorithms is to be examined with the goal of their overall comparison (using randomly generated input data).

Ingeniera Civil en Computación / Hoy en Chile, el currículo nacional para estudiantes sordos considera como idea básica de integración en la sociedad, el desarrollo pleno tanto de la Lengua de Señas chilena como del Español escrito, entendiendo la primera como una herramienta vehicular de comunicación y acceso al currículo, y la segunda, como herramienta básica para acceder a las exigencias académicas de la incorporación futura a los sistemas de educación superior o laboral. Entre las tareas pendientes en cuanto a la integración de la cultura sorda se refiere, es fundamental aumentar el acceso a la educación. En este contexto se desarrolló la aplicación web llamada Diccionario Multimedia INDESOR , herramienta colaborativa que enseña y facilita el aprendizaje de ambas lenguas, tanto para sordos como para oyentes, y que busca además reforzar el desarrollo de las habilidades de lectura y escritura en niños con déficit auditivo pertenecientes al primer y segundo ciclo de enseñanza básica. Esta aplicación consiste en un diccionario de libre acceso, que por cada palabra contiene su definición y un video de la seña que la representa. En torno a ésta, se creó una comunidad virtual de estudiantes, apoderados y profesionales del Instituto de la Sordera INDESOR, cuya capacidad de autogestión permite la mantención de información actualizada y de calidad dentro del sitio. Los usuarios sordos y oyentes de esta comunidad son los encargados de subir, descargar y evaluar el material del diccionario, mientras que los usuarios expertos (profesionales del INDESOR) se encargan de la aprobación o rechazo del mismo. Estas interacciones están equilibradas de tal forma de asegurar el crecimiento en volumen de la base de datos, imponiendo un modelo de puntaje intuitivo para los usuarios de la aplicación. El resultado de este trabajo, la creación de una plataforma web con cerca de 500 palabras, con una dinámica de interacción que permite a usuarios sordos y oyentes participar activamente dentro del sitio, cuyo potencial de crecimiento va en aumento. Así, desde la base de un diccionario, se genera un nuevo enfoque para el desarrollo de habilidades de comunicación, tanto para la comunidad sorda como para su entorno educativo.

In this thesis different situations are considered in which the preliminary test estimator is applied and the performance of the preliminary test estimator under different proposed loss functions, namely the reflected normal , linear exponential (LINEX) and bounded LINEX (BLINEX) loss functions is evaluated. In order to motivate the use of the BLINEX loss function rather than the reflected normal loss or the LINEX loss function, the risk for the preliminary test estimator and its component estimators derived under BLINEX loss is compared to the risk of the preliminary test estimator and its components estimators derived under both reflected normal loss and LINEX loss analytically (in some sections) and computationally. It is shown that both the risk under reflected normal loss and the risk under LINEX loss is higher than the risk under BLINEX loss. The key focus point under consideration is the estimation of the regression coefficients of a multiple regression model under two conditions, namely the presence of multicollinearity and linear restrictions imposed on the regression coefficients. In order to address the multicollinearity problem, the regression coefficients were adjusted by making use of Hoerl and Kennard’s (1970) approach in ridge regression. Furthermore, in situations where under- or overestimation exist, symmetric loss functions will not give optimal results and it was necessary to consider asymmetric loss functions. In the economic application, it was shown that a loss function which is both asymmetric and bounded to ensure a maximum upper bound for the loss, is the most appropriate function to use. In order to evaluate the effect that different ridge parameters have on the estimation, the risk values were calculated for all three ridge regression estimators under different conditions, namely an increase in variance, an increase in the level of multicollinearity, an increase in the number of parameters to be estimated in the regression model and an increase in the sample size. These results were compared to each other and summarised for all the proposed estimators and proposed loss functions. The comparison of the three proposed ridge regression estimators under all the proposed loss functions was also summarised for an increase in the sample size and an increase in variance. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Statistics / PhD / Unrestricted

Semi-supervised self-learning algorithms have been shown to improve classifier accuracy under a variety of conditions. In this thesis, semi-supervised self-learning using ensembles of random forests and fuzzy c-means clustering similarity was applied to three data sets to show where improvement is possible over random forests alone. Two of the data sets are emulations of large simulations in which the data may be distributed. Additionally, the ratio of majority to minority class examples in the training set was altered to examine the effect of training set bias on performance when applying the semi-supervised algorithm.

The role of topography on the spatial distribution of tornadoes was assessed through geospatial and statistical techniques. A 100-m digital elevation model was used to create slope, aspect, and surface roughness maps; and; tornado beginning and ending points and paths were used to extract terrain information. Tornado touchdowns, liftoffs, paths, and path-land angles were examined to determine whether tornado paths occur more frequently in or along certain terrain or slopes. Statistical analyses, such as bootstrapping, were used to analyze tornado touchdowns, liftoffs and paths and path-relative terrain angles. Results show that tornado paths are more common with downhill-movement. Tornadoes are not as likely to move uphill because the 73.6 percent northeast path bias represents the highest frequencies of path-angles. Tornado touchdowns and paths occur more often in smooth terrain, rather than rough terrain. Complex topographic variability seems to not have an effect on the spatial distribution of tornadoes.

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The two sample t-test is the test usually taught in introductory statistics courses to test for the equality of means of two populations. However, the t-test is not the only test available to compare the means of two populations. The randomization test is being incorporated into some introductory courses. There is also the bootstrap test. It is also not uncommon to decide the equality of the means based on confidence intervals for the means of these two populations. Are all those methods equally powerful? Can the idea of non-overlapping t confidence intervals be extended to bootstrap confidence intervals? The powers of seven alternative ways of comparing two population means are analyzed using small samples with data coming from distributions with different degrees of skewness and kurtosis. The analysis is done using simulation; programs in GAUSS were especially written for this purpose.

People at risk for blood clots are often treated with anticoagulants, warfarin is such an anticoagulant. The dose's effect is measured by comparing the time for blood to clot to a control time called an INR value. Previous anticoagulant studies have addressed agreement between fingerstick (POC) devices and the standard laboratory, however these studies rely on mathematical formulas as criteria for clinical evaluations, i.e. clinical evaluation vs. precision and bias. Fourteen such criteria were found in the literature. There exists little consistency among these criteria for assessing clinical agreement, furthermore whether these methods of assessing agreement are reasonable estimates of clinical decision-making is unknown and has yet to be validated. One previous study compared actual clinical agreement by having two physicians indicate a dosing decision based on patient history and INR values. This analysis attempts to justify previously used mathematical criteria for clinical agreement. Generalized additive models with smoothing spline estimates were calculated for each of the 14 criteria and compared to the smoothing spline estimate for the method using actual physician decisions (considered the "gold standard"). The area between the criteria method spline and the gold standard method spline served as the comparison, using bootstrapping for statistical inference. Although some of the criteria methods performed better than others, none of them matched the gold standard. This stresses the need for clinical assessment of devices.

As item response theory (IRT) has developed and is widely applied, investigating the fit of a parametric model becomes an important part of the measurement process when implementing IRT. The usefulness and successes of IRT applications rely heavily on the extent to which the model reflects the data, so it is necessary to evaluate model-data fit by gathering sufficient evidence before any model application. There is a lack of promising solutions on the detection of model misfit in IRT. In addition, commonly used fit statistics are not satisfactory in that they often do not possess desirable statistical properties and lack a means of examining the magnitude of misfit (e.g., via graphical inspections). In this dissertation, a newly-proposed nonparametric approach, RISE was thoroughly and comprehensively studied. Specifically, the purposes of this study are to (a) examine the promising fit procedure, RISE, (b) compare the statistical properties of RISE with that of the commonly used goodness-of-fit procedures, and (c) investigate how RISE may be used to examine the consequences of model misfit. To reach the above-mentioned goals, both a simulation study and empirical study were conducted. In the simulation study, four factors including ability distribution, sample size, test length and model were varied as the factors which may influence the performance of a fit statistic. The results demonstrated that RISE outperformed G2 and S-X2 in that it controlled Type I error rates and provided adequate power under all conditions. In the empirical study, the three fit statistics were applied to one empirical data and the misfitting items were flagged. RISE and S-X2 detected reasonable numbers of misfitting items while G2 detected almost all items when sample size is large. To further demonstrate an advantage of RISE, the residual plot on each misfitting item was shown. Compared to G2 and S-X2, RISE gave a much clearer picture of the location and magnitude of misfit for each misfitting item. Other than statistical properties and graphical displays, the score distribution and test characteristic curve (TCC) were investigated as model misfit consequence. The results indicated that for the given data, there was no practical consequence on classification before and after replacement of misfitting items detected by three fit statistics.

No description available.