This thesis focuses on development of spline-based hazard estimation models for cure rate data. Such data can be found in survival studies with long term survivors. Consequently, the population consists of the susceptible and non-susceptible sub-populations with the latter termed as "cured". The modeling of both the cure probability and the hazard function of the susceptible sub-population is of practical interest. Here we propose two smoothing-splines based models falling respectively into the popular classes of two component mixture cure rate models and promotion time cure rate models. Under the framework of two component mixture cure rate model, Wang, Du and Liang (2012) have developed a nonparametric model where the covariate effects on both the cure probability and the hazard component are estimated by smoothing splines. Our first development falls under the same framework but estimates the hazard component based on the accelerated failure time model, instead of the proportional hazards model in Wang, Du and Liang (2012). Our new model has better interpretation in practice. The promotion time cure rate model, motivated from a simplified biological interpretation of cancer metastasis, was first proposed only a few decades ago. Nonetheless, it has quickly become a competitor to the mixture models. Our second development aims to provide a nonparametric alternative to the existing parametric or semiparametric promotion time models. / Ph. D.

Recent theoretical and experimental studies in a wide range of applications (ultrasonics, underwater acoustics, seismicoe) have demonstrated that Green's functions (impulse responses) can be extracted from cross-correlation of diffuse fields using only passive sensors. The technique, whose validity is supported by a physical argument based on time-reversal invariance, effectively uses a correlation process between the point source and points located in the focal zone. Indeed, the coherent noise source distributions can be considered as a timereversal mirror and the cross-correlation operations gives the field measured at one receiver after refocusing on the other receiver. Passive-only reconstruction of coherent Lamb waves (80-200 kHz) in an aluminum plate and thickness comparable to aircraft fuselage and wing panels will be presented. In particular, the influence of the noise source characteristics (location, frequency spectrum) on the signal-to-noise ratio the emerging coherent waveform will be investigated using a scanning laser Doppler velocimeter. This study suggests the potential for a structural health monitoring method for aircraft panels based on passive ultrasound imaging reconstructed from diffuse fields.

In this thesis, a new trading strategy is proposed. By the help of quantile regression, the conditional distribution functions of stock market returns are estimated. Based on the knowledge of the distribution the strategy produced buying and selling signals which together with a weight function derived from exponential moving averages determines how much and when to buy or sell. The strategy performs better than the market in terms of absolute return and the Sharpe ratio in-sample, but it does not provide satisfactory results out-of-sample.

A significant progress in the evolution of the computer systems and their interconnection over the past 70 years has allowed replacing the frequently used centralized architectures with the highly distributed ones, formed by independent entities fulfilling specific functionalities as one user-intransparent unit. This has resulted in an intense scientic interest in distributed algorithms and their frequent implementation into real systems. Especially, distributed algorithms for multi-sensor data fusion, ensuring an enhanced QoS of executed applications, find a wide usage. This doctoral thesis addresses an optimization and an analysis of the distributed systems, namely the distributed consensus-based algorithms for an aggregate function estimation (primarily, my attention is focused on a mean estimation). The first section is concerned with a theoretical background of the distributed systems, their evolution, their architectures, and a comparison with the centralized systems (i.e. their advantages/disadvantages). The second chapter deals with multi-sensor data fusion, its application, the classification of the distributed estimation techniques, their mathematical modeling, and frequently quoted algorithms for distributed averaging (e.g. protocol Push-Sum, Metropolis-Hastings weights, Best Constant weights etc.). The practical part is focused on mechanisms for an optimization of the distributed systems, the proposal of novel algorithms and complements for the distributed systems, their analysis, and comparative studies in terms of such as the convergence rate, the estimation precision, the robustness, the applicability to real systems etc.

This thesis is concerned with identifying the best decision among a set of possible decisions in the presence of uncertainty. We are primarily interested in situations where the objective function value at any feasible solution needs to be estimated, for example via a ``black-box' simulation procedure. We develop adaptive random search methods for solving such simulation optimization problems. The methods are adaptive in the sense that they use information gathered during previous iterations to decide how simulation effort is expended in the current iteration. We consider random search because such methods assume very little about the structure of the underlying problem, and hence can be applied to solve complex simulation optimization problems with little expertise required from an end-user. Consequently, such methods are suitable for inclusion in simulation software. We first identify desirable features that algorithms for discrete simulation optimization need to possess to exhibit attractive empirical performance. Our approach emphasizes maintaining an appropriate balance between exploration, exploitation, and estimation. We also present two new and almost surely convergent random search methods that possess these desirable features and demonstrate their empirical attractiveness. Second, we develop two frameworks for designing adaptive and almost surely convergent random search methods for discrete simulation optimization. Our frameworks involve averaging, in that all decisions that require estimates of the objective function values at various feasible solutions are based on the averages of all observations collected at these solutions so far. We present two new and almost surely convergent variants of simulated annealing and demonstrate the empirical effectiveness of averaging and adaptivity in the context of simulated annealing. Finally, we present three random search methods for solving simulation optimization problems with uncountable feasible regions. One of the approaches is adaptive, while the other two are based on pure random search. We provide conditions under which the three methods are convergent, both in probability and almost surely. Lastly, we include a computational study that demonstrates the effectiveness of the methods when compared to some other approaches available in the literature.

No description available.