Network Tomography: Identifiability and Fourier Domain Estimation

The statistical problem for network tomography is to infer the distribution of $\mathbf{X}$, with mutually independent components, from a measurement model $\mathbf{Y}=A\mathbf{X}$, where $A$ is a given binary matrix representing the routing topology of a network under consideration. The challenge is that the dimension of $\mathbf{X}$ is much larger than that of $\mathbf{Y}$ and thus the problem is often called ill-posed. This paper studies some statistical aspects of network tomography. We first address the identifiability issue and prove that the $\mathbf{X}$ distribution is identifiable up to a shift parameter under mild conditions. We then use a mixture model of characteristic functions to derive a fast algorithm for estimating the distribution of $\mathbf{X}$ based on the General method of Moments. Through extensive model simulation and real Internet trace driven simulation, the proposed approach is shown to be favorable comparing to previous methods using simple discretization for inferring link delays in a heterogeneous network.Comment: 21 page

Categorical data analysis using a skewed Weibull regression model

In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and complementary log-log) can be obtained as limiting cases. We further compare the proposed model with some other asymmetrical models. The Bayesian as well as frequentist estimation procedures for binomial and multinomial data responses are presented in details. The analysis of two data sets to show the efficiency of the proposed model is performed

Flexible Regression Models for Survival Data

Survival analysis is a branch of statistics to analyze the time-to-event data or survival data. One important feature of survival data is censoring, which means that not all the subjects’ survival time are observed directly. Among all the survival data, right-censored data are the most common type and consist of some exactly observed survival times and some right-censored observations. In this dissertation, we focus on studying flexible regression models for complicated right-censored survival data when the classical proportional hazards (PH) assumption is not satisfied. Flexible semiparametric regression models can largely avoid misspecification of parametric distributions and thus provide more modeling flexibility. Cure models are studied in this dissertation to analyze survival data, for which there is a cured group in the study population and this is evidenced by a level-off at the end of the nonparametric survival estimate. In addition, we also incorporate background mortality in the cure models to improve estimation accuracy in this research. Considering the background mortality is important based on the fact that patients dying from other causes also benefit from the treatment of the disease of interest as shown in the SEER cancer studies. In Chapter 2, a semiparametric estimation approach is proposed based on EM algorithm under the mixture cure proportional hazards model with background mortality (MCPH+BM). In Chapter 3, a promotion time cure proportional hazards model with background mortality (PTPH+BM) is proposed, and its extension to the semiparametric transformation model is under further exploration. Both models are validated via comprehensive simulation studies and real data analysis. Another perspective on non-proportional hazards is to explore a more general model than the Cox PH model such as the generalized odds-rate (GOR) models (Dabrowska and Doksum, 1988). In Chapter 4, the identifiability problems and the estimation of parameters in the GOR models are discussed