Queen's UniversityInformation http://hdl.handle.net/1974/6 2013-05-21T08:51:12Z 2013-05-21T08:51:12Z Asoodeh, Shahab http://hdl.handle.net/1974/7819 2013-02-20T06:09:06Z 2013-02-19T05:00:00Z

Title: Feed-Forward Rate Distortion Function and Markov Sources Authors: Asoodeh, Shahab Abstract: The problem of channel coding with feedback has been extensively studied over the last 50 years. Using an ideal feedback link, the encoder knows all previously received channel outputs. Recently the duality between channel coding and rate distortion has been established in [15] and [3], leading to the problem of source coding with feed-forward. In this project we first study the general formula for the feed-forward rate distortion function given by Venkataramanan et al. [8]. They studied the source coding problem when a feed-forward link is available for general sources and general distortion measures. They derived the feed-forward rate distortion function for an arbitrary source in terms of the directed information which was originally introduced by Massey [5]. It is shown that the general formula given for source coding with feed-forward is closely related to the general formula for channel coding with feedback given by Tatikonda [4]. We then study another formula for the feed-forward rate distortion function recently proposed by Naiss et al. which is tractable and computable [17]. They also calculated the exact rate distortion function for first order asymmetric Markov sources. An original contribution of this project is an alternative achievability proof for the feed-forward rate distortion function of first order asymmetric Markov sources.

2013-02-19T05:00:00Z NIU, YI http://hdl.handle.net/1974/7796 2013-02-02T06:05:06Z 2013-02-01T05:00:00Z

Title: Marginal Models for Modeling Clustered Failure Time Data Authors: NIU, YI Abstract: Clustered failure time data often arise in biomedical and clinical studies where potential correlation among survival times is induced in a cluster. In this thesis, we develop a class of marginal models for right censored clustered failure time data and propose a novel generalized estimating equation approach in a likelihood-based context. We first investigate a semiparametric proportional hazards model for clustered survival data and derive the large sample properties of the regression estimators. The finite sample studies demonstrate that the good applicability of the proposed method as well as the substantial efficiency improvement in comparison with the existing marginal model for clustered survival data. Another important feature of failure time data we will consider in this thesis is a possible fraction of cured subjects. To accommodate the potential cure fraction, we consider a proportional hazards mixture cure model for clustered survival data with long-term survivors and develop a set of estimating equations by incorporating working correlation matrices in an EM algorithm. The dependence among the cure statuses and among the survival times of uncured patients within clusters are modeled by working correlation matrices in the estimating equations. For the parametric proportional hazards mixture cure model, we show that the estimators of the regression parameters and the parameter in the baseline hazard function are consistent and asymptotically normal with a sandwich covariance matrix that can be consistently estimated. A numerical study presents that the proposed estimation method is comparable with the existing parametric marginal method. We also extend the proposed generalized estimating equation approach to a semiparametric proportional hazards mixture cure model where the baseline survival function is nonparametrically specified. A bootstrap method is used to obtain the variances of the estimates. The proposed method is evaluated by a simulation study from which we observe a noticeable efficiency gain of the proposed method over the existing semiparametric marginal method for clustered failure time data with a cure fraction. Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-01-30 21:23:48.968

2013-02-01T05:00:00Z Song, Hui http://hdl.handle.net/1974/7759 2013-01-24T06:10:20Z 2013-01-23T05:00:00Z

Title: Joint Modelling of Longitudinal Quality of Life Measurements and Survival Data in Cancer Clinical Trials Authors: Song, Hui Abstract: In cancer clinical trials, longitudinal Quality of Life (QoL) measurements on a patient may be analyzed by classical linear mixed models but some patients may drop out of study due to recurrence or death, which causes problems in the application of classical methods. Joint modelling of longitudinal QoL measurements and survival times may be employed to explain the dropout information of longitudinal QoL measurements, and provide more efficient estimation, especially when there is strong association between longitudinal measurements and survival times. Most joint models in the literature assumed classical linear mixed model for longitudinal measurements, and Cox's proportional hazards model for survival times. The linear mixed model with normal-distribution random effects may not be sufficient to model longitudinal QoL measurements. Moreover, with advances in medical research, long-term survivors may exist, which makes the proportional hazards assumption not suitable for survival times when some censoring times are due to potential cured patients. In this thesis, we propose new models to analyze longitudinal QoL measurements and survival times jointly. In the first part of this thesis, we develop a joint model which assumes a linear mixed tt model for longitudinal measurements and a promotion time cure model for survival data. We link these two models through a latent variable and develop a semiparametric inference procedure. The second part of this thesis considers a special feature of the QoL measurements. That is, they are constrained in an interval (0,1). We propose to take into account this feature by a simplex-distribution model for these QoL measurements. Classical proportional hazards and promotion time cure models are used separately to the situations, depending on whether a cure fraction is assumed in the data or not. In both cases, we characterize the correlation between the longitudinal measurements and survival times by a shared random effect, and derive a semiparametric penalized joint partial likelihood to estimate the parameters. The above proposed new joint models and estimation procedures are evaluated in simulation studies and applied to the QoL measurements and recurrence times from a clinical trial on women with early breast cancer. Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-01-23 14:04:14.297

2013-01-23T05:00:00Z Johnston, Andrew http://hdl.handle.net/1974/7684 2012-12-07T06:06:26Z 2012-12-06T05:00:00Z

Title: Networked Control Systems with Unbounded Noise under Information Constraints Authors: Johnston, Andrew Abstract: We investigate the stabilization of unstable multidimensional partially observed single-station, multi-sensor (single-controller) and multi-controller (single-sensor) linear systems controlled over discrete noiseless channels under fixed-rate information constraints. Stability is achieved under communication requirements that are asymptotically tight in the limit of large sampling periods. Through the use of similarity transforms, sampling and random-time drift conditions we obtain a coding and control policy leading to the existence of a unique invariant distribution and finite second moment for the sampled state. We use a vector stabilization scheme in which all modes of the linear system visit a compact set together infinitely often. Description: Thesis (Master, Mathematics & Statistics) -- Queen's University, 2012-12-06 15:06:37.449

2012-12-06T05:00:00Z