No description available.

Medical cost analysis is an important part of treatment evaluation. Since resources are limited in society, it is important new treatments are developed with proper costconsiderations. The mean has been mostly accepted as a measure of the medical cost analysis. However, it is well known that cost data is highly skewed and the mean could be highly influenced by outliers. Therefore, in many situations the mean cost alone cannot offer complete information about medical costs. The quantiles (e.g., the first quartile, median and third quartile) of medical costs could better represent the typical costs paid by a group of individuals, and could provide additional information beyond mean cost. For a specified patient population, cost estimates are generally determined from the beginning of treatments until death or end of the study period. A number of statistical methods have been proposed to estimate medical cost. Since medical cost data are skewed to the right, normal approximation based confidence intervals can have much lower coverage probability than the desired nominal level when the cost data are moderately or severely skewed. Additionally, we note that the variance estimators of the cost estimates are analytically complicated. In order to address some of the above issues, in the first part of the dissertation we propose two empirical likelihood-based confidence intervals for the mean medical costs: One is an empirical likelihood interval (ELI) based on influence function, the other is a jackknife empirical likelihood (JEL) based interval. We prove that under very general conditions, −2log (empirical likelihood ratio) has an asymptotic standard chi squared distribution with one degree of freedom for mean medical cost. Also we show that the log-jackknife empirical likelihood ratio statistics follow standard χ2 distribution with one degree of freedom for mean medical cost. In the second part of the dissertation, we propose an influence function-based empirical likelihood method to construct a confidence region for the vector of regression parameters in mean cost regression models with censored data. The proposed confidence region can be used to obtain a confidence interval for the expected total cost of a patient with given covariates. The new method has sound asymptotic property (Wilks Theorem). In the third part of the dissertation we propose empirical likelihood method based on influence function to construct confidence intervals for quantile medical costs with censored data. We prove that under very general conditions, −2log (empirical likelihood ratio) has an asymptotic standard chi squared distribution with one degree of freedom for quantile medical cost. Simulation studies are conducted to compare coverage probabilities and interval lengths of the proposed confidence intervals with the existing confidence intervals. The proposed methods are observed to have better finite sample performances than existing methods. The new methods are also illustrated through a real example.

The consequences of substituting the denominator Q 3(p) - Q 1(p) by Q 2 - Q 1(p) in Groeneveld's class of quantile measures of kurtosis (γ 2(p)) for symmetric distributions, are explored using the symmetric influence function. The relationship between the measure γ 2(p) and the alternative class of kurtosis measures κ2(p) is derived together with the relationship between their influence functions. The Laplace, Logistic, symmetric Two-sided Power, Tukey and Beta distributions are considered in the examples in order to discuss the results obtained pertaining to unimodal, heavy tailed, bounded domain and U-shaped distributions.

No description available.

We propose new estimation methods for the factor loading matrix in modeling multivariate volatility processes. The key step of the methods is based on the weighted scatter estimators, which does not involve optimizing any objective function and was embedded with robust estimation properties. The method can therefore be easily applied to high-dimensional systems without running into computational problems. The estimation is proved to be consistent and the asymptotic distribution is derived. We compare the performance with other estimation methods and demonstrate its superiority when using both simulated data as well as real-world case studies. / Statistics

In die Infrastruktur unserer Gesellschaft sind komplexe IT-Systeme fest eingebettet. Die Verbreitung und Verstetigung von IT-Systemen betrifft zentrale Bereiche unserer Gesellschaft beispielsweise Verkehrs-, Finanz- oder Gesundheitssystem. Lange Zeit standen funktionale Aspekte bei der Entwicklung informationstechnischer Systeme im Vordergrund. In den letzten Jahren haben sich jedoch nichtfunktionale Eigenschaften von IT-Systemen wie Robustheit zu unverzichtbaren Schlüsseleigenschaften in einer Vielzahl von Anwendungsfeldern entwickelt. Systeme während der Betriebsphase sind Veränderungen der gegebenen Einsatz- und Betriebsbedingungen durch Störungen der Umgebung oder auch Verschleißerscheinungen ausgesetzt. Ziel der Forschungsarbeit ist es ein Konzept für die Systemeigenschaft Robustheit zu entwickeln. Für ein gegebenes System mit einem definierten Funktionsziel ist zu analysieren, inwieweit es robust hinsichtlich Störungen der Einsatzbedingungen, verursacht durch Ereignisse der Umgebung, ist und folglich trotzdem das Funktionsziel erfüllt. Das vorgestellte Konzept umfasst dabei zwei wesentliche Problemstellungen: Bewertung der Robustheit Methode für robuste Systeme zur Laufzeit In Abhängigkeit der technischen Kennzahl, Robustheit, wird eine optimale Entscheidungsstrategie gewählt und so das Systemverhalten gesteuert. Mit der Integration eines Robustheitskonzepts insbesondere für den Systembetrieb soll anhand der Berücksichtigung der Systemeigenschaft Robustheit zur Laufzeit ein Beitrag zum Qualitätszuwachs bei Systemen geleistet werden. / Complex IT-systems are deeply embedded in the infrastructure of the society. The integration of these systems is important for plenty of areas such as the transportation system, the financial system or the health care system. For a long time, the functional aspects of the invention had been put forward. But lately the non-functional characteristics of IT-systems such as robustness have developed to essential key factors in many fields. A lot of systems are being exposed to environmental disturbances are showing during the stage of operation. This research work purpose is to develop a concept of robustness to increase system robustness. The robustness of embedded systems is supposed to be analyzed towards disturbances and terms of usage that were caused by the environment. Thereby the concept targets two main issues: measurement of the robustness and methods for robust systems concerning its duration. Depending on the value of robustness a proper decision is made in order to control the behavior of the system. Through an integration of the above mentioned concept, a rise of quality regarding the robustness of the system is pursued respecting its period of operation.

This thesis includes three chapters regarding influence functions, higher moments, and futures hedging. In Chapter 2, the objective is to use an influence function to better understand semi-kurtosis for use in analyzing peakedness and tail heaviness on one side of a distribution. Also, it is shown that both the right side semi-kurtosis and left side semi-kurtosis summed together, equal kurtosis, so the ratio of semi-kurtosis to kurtosis can be used to analyze asymmetry, as an alternative to skewness. In Chapter 3, the objective is to analyze higher moments of daily, weekly, and monthly stock market returns using large stocks, technology stocks, and small cap stocks. Kurtosis is found to be positive (greater than 3) and statistically significant for all of the daily and weekly stock market returns, indicating peakedness and fat tails. Similar to kurtosis, the left side semi-fourth moment (semi-kurtosis) is also found to be positive (greater than 1.5) for all of daily and weekly returns, indicating peakedness and fat tails on the left sides of the distributions. Skewness is found to be both positive and negative in the daily stock returns data, indicating asymmetry but with no consistent patterns. The fifth moment is also used to analyze asymmetry, as an alternative to skewness. The fifth moment and skewness (third moment) sometimes indicate opposite asymmetry results, as evidenced by different signs for the two moments. This is because the exponent of five for the fifth moment amplifies observations further from the mean, more so than the exponent of three for skewness. In Chapter 4, the objective is to analyze research on futures hedging and to identify the major factors affecting the use of futures hedging by commodity producers. A multifactor conceptual model is developed that explains the factors and subfactors that are likely to affect the commodity producers’ hedging decisions. Factors include industry characteristics, business operation characteristics, management characteristics, futures hedging costs, and substitute risk management instruments. This model provides a more complete understanding of the factors and subfactors affecting futures hedging, and should be of interest to academics and practitioners working with hedging models.

This thesis includes three chapters regarding influence functions, higher moments, and futures hedging. In Chapter 2, the objective is to use an influence function to better understand semi-kurtosis for use in analyzing peakedness and tail heaviness on one side of a distribution. Also, it is shown that both the right side semi-kurtosis and left side semi-kurtosis summed together, equal kurtosis, so the ratio of semi-kurtosis to kurtosis can be used to analyze asymmetry, as an alternative to skewness. In Chapter 3, the objective is to analyze higher moments of daily, weekly, and monthly stock market returns using large stocks, technology stocks, and small cap stocks. Kurtosis is found to be positive (greater than 3) and statistically significant for all of the daily and weekly stock market returns, indicating peakedness and fat tails. Similar to kurtosis, the left side semi-fourth moment (semi-kurtosis) is also found to be positive (greater than 1.5) for all of daily and weekly returns, indicating peakedness and fat tails on the left sides of the distributions. Skewness is found to be both positive and negative in the daily stock returns data, indicating asymmetry but with no consistent patterns. The fifth moment is also used to analyze asymmetry, as an alternative to skewness. The fifth moment and skewness (third moment) sometimes indicate opposite asymmetry results, as evidenced by different signs for the two moments. This is because the exponent of five for the fifth moment amplifies observations further from the mean, more so than the exponent of three for skewness. In Chapter 4, the objective is to analyze research on futures hedging and to identify the major factors affecting the use of futures hedging by commodity producers. A multifactor conceptual model is developed that explains the factors and subfactors that are likely to affect the commodity producers’ hedging decisions. Factors include industry characteristics, business operation characteristics, management characteristics, futures hedging costs, and substitute risk management instruments. This model provides a more complete understanding of the factors and subfactors affecting futures hedging, and should be of interest to academics and practitioners working with hedging models.

In die Infrastruktur unserer Gesellschaft sind komplexe IT-Systeme fest eingebettet. Die Verbreitung und Verstetigung von IT-Systemen betrifft zentrale Bereiche unserer Gesellschaft beispielsweise Verkehrs-, Finanz- oder Gesundheitssystem. Lange Zeit standen funktionale Aspekte bei der Entwicklung informationstechnischer Systeme im Vordergrund. In den letzten Jahren haben sich jedoch nichtfunktionale Eigenschaften von IT-Systemen wie Robustheit zu unverzichtbaren Schlüsseleigenschaften in einer Vielzahl von Anwendungsfeldern entwickelt. Systeme während der Betriebsphase sind Veränderungen der gegebenen Einsatz- und Betriebsbedingungen durch Störungen der Umgebung oder auch Verschleißerscheinungen ausgesetzt. Ziel der Forschungsarbeit ist es ein Konzept für die Systemeigenschaft Robustheit zu entwickeln. Für ein gegebenes System mit einem definierten Funktionsziel ist zu analysieren, inwieweit es robust hinsichtlich Störungen der Einsatzbedingungen, verursacht durch Ereignisse der Umgebung, ist und folglich trotzdem das Funktionsziel erfüllt. Das vorgestellte Konzept umfasst dabei zwei wesentliche Problemstellungen: Bewertung der Robustheit und Methode für robuste Systeme zur Laufzeit. In Abhängigkeit der technischen Kennzahl, Robustheit, wird eine optimale Entscheidungsstrategie gewählt und so das Systemverhalten gesteuert. Mit der Integration eines Robustheitskonzepts insbesondere für den Systembetrieb soll anhand der Berücksichtigung der Systemeigenschaft Robustheit zur Laufzeit ein Beitrag zum Qualitätszuwachs bei Systemen geleistet werden. / Complex IT-systems are deeply embedded in the infrastructure of the society. The integration of these systems is important for plenty of areas such as the transportation system, the financial system or the health care system. For a long time, the functional aspects of the invention had been put forward. But lately the non-functional characteristics of IT-systems such as robustness have developed to essential key factors in many fields. A lot of systems are being exposed to environmental disturbances are showing during the stage of operation. This research work purpose is to develop a concept of robustness to increase system robustness. The robustness of embedded systems is supposed to be analyzed towards disturbances and terms of usage that were caused by the environment. Thereby the concept targets two main issues: measurement of the robustness and methods for robust systems concerning its duration. Depending on the value of robustness a proper decision is made in order to control the behavior of the system. Through an integration of the above mentioned concept, a rise of quality regarding the robustness of the system is pursued respecting its period of operation.

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.