Inferring influence in dynamic networks and multiple sampling for estimation of fractional Brownian motion

This thesis is divided into two parts. In the first part, we focus on network influence analysis in dynamic networks. In the second part, we focus on multiple sampling methods to estimate the fractional Brownian motion strategically. In Chapter 2, we explore degrees of influence in dynamic networks. We propose a longitudinal influence model to represent how an individual's behavior can be influenced by others in dynamic networks. A sequential hypothesis testing procedure is proposed to determine the degrees of influence. We provide a theoretical justification of our proposed sequential testing procedure. Simulation studies show our testing procedure can preserve the level of the test and is more powerful for a larger network. We also apply our proposed method to detect the degrees of influence for Higgs Twitter data set and Digg2009 data set. In Chapter 3, we investigate another aspect of network influence analysis, which is influence power. The influence power describes the magnitude of influence that each node has on the other nodes in the network. In this chapter, we build a network influence autoregression model to model the influence powers among different nodes in dynamic networks. We use the maximum likelihood estimation method to estimate the parameters in the model. We show the estimation consistency of parameter estimates and demonstrate the performance of our proposed methods using simulation studies. We also illustrate the usefulness of our model by applying it to the China fiscal revenue data. In Chapter 4, we focus on multiple sampling problems for the estimation of the fractional Brownian motion when the maximum number of samples is limited, extending existing results in the literature in a non-Markovian framework. Two classes of sampling schemes are proposed: a deterministic scheme and a level-triggered scheme. For the deterministic sampling scheme, the sampling times are selected beforehand and do not depend on the process trajectory. For the level-triggered sampling scheme, the sampling times are the times when the process crosses predetermined thresholds. The sampling times are selected sequentially in time and depend on the process trajectory. For each of the schemes, we derive the optimal sampling times by minimizing the aggregate squared error distortion. We then show that the optimal sampling strategies heavily depend on the dependence structure of the process.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Cui, Xiang

Contributors dc:contributor

• Chen, Yuguo
• Chronopoulou, Alexandra
• Culpepper, Steven
• Li, Xinran

• Social influence
• Dynamic networks
• Multiple sampling
• Fractional Brownian motion

Statement dc:rights

• Copyright 2022 Xiang Cui

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115702

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115702