In statistics it is of interest to find a better interval estimator of the absolute mean deviation. In this thesis, we focus on using the jackknife, the adjusted and the extended jackknife empirical likelihood methods to construct confidence intervals for the mean absolute deviation of a random variable. The empirical log-likelihood ratio statistics is derived whose asymptotic distribution is a standard chi-square distribution. The results of simulation study show the comparison of the average length and coverage probability by using jackknife empirical likelihood methods and normal approximation method. The proposed adjusted and extended jackknife empirical likelihood methods perform better than other methods for symmetric and skewed distributions. We use real data sets to illustrate the proposed jackknife empirical likelihood methods.

This paper studies the interval estimation of three discrete distributions: thebinomial distribution, the Poisson distribution and the negative-binomialdistribution. The problem is the chaotic behavior of the coverage probabilityfor the Wald interval. To solve this problem, alternative confidence intervals areintroduced. Coverage probability and expected length are chosen to be thecriteria evaluating the intervals.In this paper, I firstly tested the chaotic behavior of the coverageprobability for the Wald interval, and introduced the alternative confidenceintervals. Then I calculated the coverage probability and expected length forthose intervals, made comparisons and recommended confidence intervals forthe three cases. This paper also discussed the relationship among the threediscrete distributions, and in the end illustrated the applications on binomialand Poisson data with brief examples.

Deploying unmanned aerial vehicle (UAV) networks to provide coverage for outdoor users has attracted great attention during the last decade. Terrain information requires extensive attention in outdoor UAV networks, and it is one of the most important factors affecting coverage performance. Providing tractable models and common methods is necessary to generalize the terrain-based outdoor UAV positioning strategies. In this thesis, we demonstrate that UAVs can provide stable coverage for regularly moving users based on the existing local terrain reconstruction methods with UAV sampling. Next, a coarse-grained UAV deployment can be performed with a simple set of parameters that characterize the terrain features. A stochastic geometry framework can provide general analytical results for the above coarse-grained UAV networks. In addition, the UAV can avoid building blockage without prior terrain information through real-time linear-trajectory search. We proposed four algorithms related to the combinations of collecting prior terrain information and using real-time search, and then their performances are evaluated and compared in different scenarios. By adjusting the height of the UAV based on terrain information collected before networking, the performance is significantly enhanced compared to the one when no terrain information is available. The algorithm based on real-time search further improves the coverage performance by avoiding the shadow of buildings. During the execution of the real-time search algorithm, the search distance is reduced using the collected terrain information.

This dissertation develops, applies, and investigates new methods to improve the analysis of logistic regression mixture models. An interesting dose-response experiment was previously carried out on a mixed population, in which the class membership of only a subset of subjects (survivors) were subsequently labeled. In early analyses of the dataset, challenges with separation of points and asymmetric confidence intervals were encountered. This dissertation extends the previous analyses by characterizing the model in terms of a mixture of penalized (Firth) logistic regressions and developing methods for constructing profile likelihood-based confidence and inverse intervals, and confidence bands in the context of such a model. The proposed methods are applied to the motivating dataset and another related dataset, resulting in improved inference on model parameters. Additionally, a simulation experiment is carried out to further illustrate the benefits of the proposed methods and to begin to explore better designs for future studies. The penalized model is shown to be less biased than the traditional model and profile likelihood-based intervals are shown to have better coverage probability than Wald-type intervals. Some limitations, extensions, and alternatives to the proposed methods are discussed.

Wireless network virtualization (WNV) and millimeter wave (mmW) communications are emerging as two key technologies for cellular networks. Virtualization in cellular networks enables wireless services to be decoupled from network resources (e.g., infrastructure and spectrum) so that multiple virtual networks can be built using a shared pool of network resources. At the same time, utilization of the large bandwidth available in mmW frequency band would help to overcome ongoing spectrum scarcity issues. In this context, this dissertation presents efficient frameworks for building virtual networks in sub-6 GHz and mmW bands. Towards developing the frameworks, first, we derive a closed-form expression for the downlink rate coverage probability of a typical sub-6 GHz cellular network with known base station (BS) locations and stochastic user equipment (UE) locations and channel conditions. Then, using the closed-form expression, we develop a sub-6 GHz virtual resource allocation framework that aggregates, slices, and allocates the sub-6 Ghz network resources to the virtual networks in such a way that the virtual networks' sub-6 GHz downlink coverage and rate demands are probabilistically satisfied while resource over-provisioning is minimized in the presence of uncertainty in UE locations and channel conditions. Furthermore, considering the possibility of lack of sufficient sub-6 GHz resources to satisfy the rate coverage demands of all virtual networks, we design a prioritized sub-6 GHz virtual resource allocation scheme where virtual networks are built sequentially based on their given priorities. To this end, we develop static frameworks that allocate sub-6 GHz resources in the presence of uncertainty in UE locations and channel conditions, i.e., before the UE locations and channel conditions are revealed. As a result, when a slice of a BS serves its associated UEs, it can be over-satisfied (i.e., resources left after satisfying the rate demands of all UEs) or under-satisfied (i.e., lack of resources to satisfy the rate demands of all UEs). On the other hand, it is extremely challenging to execute the entire virtual resource allocation process in real time due to the small transmission time intervals (TTIs) of cellular technologies. Taking this into consideration, we develop an efficient scheme that performs the virtual resource allocation in two phases, i.e., virtual network deployment phase (static) and statistical multiplexing phase (adaptive). In the virtual network deployment phase, sub-6 GHz resources are aggregated, sliced, and allocated to the virtual networks considering the presence of uncertainty in UE locations and channel conditions, without knowing which realization of UE locations and channel conditions will occur. Once the virtual networks are deployed, each of the aggregated BSs performs statistical multiplexing, i.e., allocates excess resources from the over-satisfied slices to the under-satisfied slices, according to the realized channel conditions of associated UEs. In this way, we further improve the sub-6 GHz resource utilization. Next, we steer our focus on the mmW virtual resource allocation process. MmW systems typically use beamforming techniques to compensate for the high pathloss. The directional communication in the presence of uncertainty in UE locations and channel conditions, make maintaining connectivity and performing initial access and cell discovery challenging. To address these challenges, we develop an efficient framework for mmW virtual network deployment and UE assignment. The deployment decisions (i.e., the required set of mmW BSs and their optimal beam directions) are taken in the presence of uncertainty in UE locations and channel conditions, i.e., before the UE locations and channel conditions are revealed. Once the virtual networks are deployed, an optimal mmW link (or a fallback sub-6 GHz link) is assigned to each UE according to the realized UE locations and channel conditions. Our numerical results demonstrate the gains brought by our proposed scheme in terms of minimizing resource over-provisioning while probabilistically satisfying virtual networks' sub-6 GHz and mmW demands in the presence of uncertainty in UE locations and channel conditions. / Doctor of Philosophy / In cellular networks, mobile network operators (MNOs) have been sharing resources (e.g., infrastructure and spectrum) as a solution to extend coverage, increase capacity, and decrease expenditures. Recently, due to the advent of 5G wireless services with enormous coverage and capacity demands and potential revenue losses due to over-provisioning to serve peak demands, the motivation for sharing and virtualization has significantly increased in cellular networks. Through wireless network virtualization (WNV), wireless services can be decoupled from the network resources so that various services can efficiently share the resources. At the same time, utilization of the large bandwidth available in millimeter wave (mmW) frequency band would help to overcome ongoing spectrum scarcity issues. However, due to the inherent features of cellular networks, i.e., the uncertainty in user equipment (UE) locations and channel conditions, enabling WNV and mmW communications in cellular networks is a challenging task. Specifically, we need to build the virtual networks in such a way that UE demands are satisfied, isolation among the virtual networks are maintained, and resource over-provisioning is minimized in the presence of uncertainty in UE locations and channel conditions. In addition, the mmW channels experience higher attenuation and blockage due to their small wavelengths compared to conventional sub-6 GHz channels. To compensate for the high pathloss, mmW systems typically use beamforming techniques. The directional communication in the presence of uncertainty in UE locations and channel conditions, make maintaining connectivity and performing initial access and cell discovery challenging. Our goal is to address these challenges and develop optimization frameworks to efficiently enable virtualization and mmW technologies in cellular networks.

The correlation coefficient (CC) is a standard measure of the linear association between two random variables. The CC plays a significant role in many quantitative researches. In a bivariate normal distribution, there are many types of interval estimation for CC, such as z-transformation and maximum likelihood estimation based methods. However, when the underlying bivariate distribution is unknown, the construction of confidence intervals for the CC is still not well-developed. In this thesis, we discuss various interval estimation methods for the CC. We propose a generalized confidence interval and three empirical likelihood-based non-parametric intervals for the CC. We also conduct extensive simulation studies to compare the new intervals with existing intervals in terms of coverage probability and interval length. Finally, two real examples are used to demonstrate the application of the proposed methods.

Large-scale blockages like buildings affect the performance of urban cellular networks, especially in the millimeter-wave frequency band. Unfortunately, such blockage effects are either neglected or characterized by oversimplified models in the analysis of cellular networks. Leveraging concepts from random shape theory, this paper proposes a mathematical framework to model random blockages, and quantifies their effects on the performance of cellular networks. Specifically, random buildings are modeled as a process of rectangles with random sizes and orientations whose centers form a Poisson point process on the plane, which is called a Boolean scheme. The distribution of the number of blockages in a link is proven to be Poisson with parameter dependent on the length of the link, which leads to the distribution of penetration losses of a single link. A path loss model that incorporates the blockage effects is proposed, which matches experimental trends observed in prior work. The blockage model is applied to analyze blockage effects on cellular networks assuming blockages are impenetrable, in terms of connectivity, coverage probability, and average rate. Analytic results show while buildings may block the desired signal, they may still have a positive impact on network performance since they also block more interference. / text

The estimation of low income proportions plays an important role in comparisons of poverty in different countries. In most countries, the stability of the society and the development of economics depend on the estimation of low income proportions. An accurate estimation of a low income proportion has a crucial role for the development of the natural economy and the improvement of people's living standards. In this thesis, the Jackknife empirical likelihood method is employed to construct confidence intervals for a low income proportion when the observed data had missing values. Comprehensive simulation studies are conducted to compare the relative performances of two Jackknife empirical likelihood based confidence intervals for low income proportions in terms of coverage probability. A real data example is used to illustrate the application of the proposed methods.

In this thesis, we study two methods for inference of parameters in the accelerated failure time model with right censoring data. One is the Wald-type method, which involves parameter estimation. The other one is empirical likelihood method, which is based on the asymptotic distribution of likelihood ratio. We employ a monotone censored data version of Kendall estimating equation, and construct confidence intervals from both methods. In the simulation studies, we compare the empirical likelihood (EL) and the Wald-type procedure in terms of coverage accuracy and average length of confidence intervals. It is concluded that the empirical likelihood method has a better performance. We also compare the EL for Kendall’s rank regression estimator with the EL for other well known estimators and find advantages of the EL for Kendall estimator for small size sample. Finally, a real clinical trial data is used for the purpose of illustration.

Cox Proportional Hazard Model is one of the most popular tools used in the study of Survival Analysis. Empirical Likelihood (EL) method has been used to study the Cox Proportional Hazard Model. In recent work by Qin and Jing (2001), empirical likelihood based confidence region is constructed with the assumption that the baseline hazard function is known. However, in Cox’s regression model the baseline hazard function is unspecified. In this thesis, we re-formulate empirical likelihood for the vector of regression parameters by estimating the baseline hazard function. The EL confidence regions are obtained accordingly. In addition, Adjusted Empirical Likelihood (AEL) method is proposed. Furthermore, we conduct extensive simulation studies to evaluate the performance of the proposed empirical likelihood methods in terms of coverage probabilities by comparing with the Normal Approximation based method. The simulation studies show that all the three methods produce similar coverage probabilities.