Mathematics Commons^™

Infinite-Dimensional Traits: Estimation Of Mean, Covariance, And Selection Gradient Of Tribolium Castaneum Growth Curves, Ly Viet Hoang

Theses and Dissertations

In evolutionary biology, traits like growth curves, reaction norms or morphological shapes cannot be described by a finite vector of components alone. Instead, continuous functions represent a more useful structure. Such traits are called function-valued or infinite-dimensional traits. Kirkpatrick and Heckmann outlined the first quantitative genetic model for these traits. Beder and Gomulkiewicz extended the theory on the selection gradient and the evolutionary response from finite- to infinite-dimensional traits.

Rigorous methods for the estimation of these quantities were developed throughout the years. In his dissertation, Baur defines estimators for the mean and covariance function, as well as for the selection …

Robust And Computationally Efficient Methods For Fitting Loss Models And Pricing Insurance Risks, Qian Zhao

Theses and Dissertations

Continuous parametric distributions are useful tools for modeling and pricing insurance risks, measuring income inequality in economics, investigating reliability of engineering systems, and in many other areas of application. In this dissertation, we propose and develop a new method for estimation of their parameters—the method of Winsorized moments (MWM)—which is conceptually similar to the method of trimmed moments (MTM) and thus is robust and computationally efficient. Both approaches yield explicit formulas of parameter estimators for location-scale and log-location-scale families, which are commonly used to model claim severity. Large-sample properties of the new estimators are provided and corroborated through simulations. Their …

Associated Hypothesis In Linear Models With Unbalanced Data, Rica Katharina Wedowski

Theses and Dissertations

In a two-way linear model one can test six different hypotheses regarding the effects in this model. Those hypotheses can be ranked from less specific to more specific. Therefore the more specific hypotheses are nested in the less specific ones. To test those nested hypotheses sequential sums of squares are used. Searle sees a problem with these since they test an associated hypothesis that has the same sums of squares but involve the sample sizes. Hypotheses should be generic and not dependent on the data. The proof he uses in his book Linear Models for Unbalanced Data is not easy …

Black-Scholes Model: An Analysis Of The Influence Of Volatility, Cornelia Krome

Theses and Dissertations

In this thesis the influence of volatility in the Black-Scholes model is analyzed. The deduced Black-Scholes formula estimates the price of European options. Contrary to the other parameters of the formula, the future volatility of the underlying asset cannot be observed in the market. The parameter needs to be assumed in order to calculate the option price. An inaccurate assumption may lead to an erroneous volatility. It is studied how a falsely assumed volatility impacts on the option price. Empirical simulations will be carried out to get an impression of possible errors in the computations. Afterwards, those results will be …