For a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a non-parametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error distributions. Under the alternative hypothesis with a change-point, the comparisons with two other methods (Chen's SIC method and Muggeo's SEG method) show that the proposed method performs better when the slope change is small. A power analysis is conducted to illustrate the performance of the test. The proposed method is also applied to analyze two real datasets: the plasma osmolality dataset and the gasoline price dataset. / by Zhihua Liu. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 200?. Mode of access: World Wide Web.

The convex hull of a sample is used to approximate the support of the underlying distribution. This approximation has many practical implications in real life. For example, approximating the boundary of a finite set is used by many authors in environmental studies and medical research. To approximate the functionals of convex hulls, asymptotic theory plays a crucial role. Unfortunately, the asymptotic results are mostly very complicated. To address this complication, we suggest a consistent bootstrapping scheme for certain cases. Our resampling technique is used for both semi-parametric and non-parametric cases. Let X1,X2,...,Xn be a sequence of i.i.d. random points uniformly distributed on an unknown convex set. Our bootstrapping scheme relies on resampling uniformly from the convex hull of X1,X2,...,Xn. In this thesis, we study the asymptotic consistency of certain functionals of convex hulls. In particular, we apply our bootstrapping technique to the Hausdorff distance between the actual convex set and its estimator. We also provide a conjecture for the application of our bootstrapping scheme to Gaussian polytopes. Moreover, some other relevant consistency results for the regular bootstrap are developed.

As ubiquitous wireless communication becomes part of life, the demand on antenna miniaturization and interference reduction becomes more extreme. However, antenna size and performance are limited by radiation physics, not technology. In order to understand antenna radiation and energy storage mechanisms, classical and alternative viewpoints of radiation are discussed. Unlike the common sense of classical antenna radiation, it is shown that the entire antenna fields contribute to both radiation and energy storage with varying total energy velocity during the radiation process. These observations were obtained through investigating impedance, power, the Poynting vector, and energy velocity of a radiating antenna. Antenna transfer functions were investigated to understand the real-world challenges in antenna design and overall performance. An extended model, using both the singularity expansion method and spherical mode decomposition, is introduced to analyze the characteristics of various antenna types including resonant, frequency-independent, and ultra-wideband antennas. It is shown that the extended model is useful to understand real-world antennas. Observations from antenna radiation physics and transfer function modeling lead to both corrections and extension of the classical fundamental-limit theory on antenna size. Both field and circuit viewpoints of the corrected limit theory are presented. The corrected theory is extended for multi-mode excitation cases and also for ultra-wideband and frequency-independent antennas. Further investigation on the fundamental-limit theory provides new innovations, including a low-Q antenna design approach that reduces antenna interference issues and a generalized approach for designing an antenna close to the theoretical-size limit. Design examples applying these new approaches with simulations and measurements are presented. The extended limit theory and developed antenna design approaches will find many applications to optimize compact antenna solutions with reduced near-field interactions. / Ph. D.

In this paper I derive the asymptotics of the exact, Euler, and Milstein ML estimators for diffusion models, including general nonstationary diffusions. Though there have been many estimators for the diffusion model, their asymptotic properties were generally unknown. This is especially true for the nonstationary processes, even though they are usually far from the standard ones. Using a new asymptotics with respect to both the time span T and the sampling interval ¢, I find the asymptotics of the estimators and also derive the conditions for the consistency. With this new asymptotic result, I could show that this result can explain the properties of the estimators more correctly than the existing asymptotics with respect only to the sample size n. I also show that there are many possibilities to get a better estimator utilizing this asymptotic result with a couple of examples, and in the second part of the paper, I derive the higher order asymptotics which can be used in the bootstrap analysis.