Abstract

Past few decades have witnessed skyrocketed development of modern technologies. As a result, data collected from modern technologies are evolving towards a direction with more complicated structure and larger scale, driving the traditional data analysis methods to develop and adapt. In this dissertation, we study three statistical issues rising in data with complicated structure and/or in large scale. In Chapter 2, we propose a Bayesian framework via exponential random graph models (ERGM) to estimate the model parameters and network structures for networks with measurement errors; In Chapter 3, we design a novel network sampling algorithm for large-scale networks with community structure; In Chapter 4, we introduce a proper framework to conduct discrete large-scale hypothesis testing procedure based on local false discovery rate (FDR). The performances of our procedures are evaluated through various simulations and real applications, while necessary theoretical properties are carefully studied as well.

Committee Chair

Nan Lin

Committee Members

Likai Chen, Jimin Ding, Jose Figueroa-Lopez, Jingqin Luo,

Comments

Permanent URL: https://doi.org/10.7936/fvzv-p904

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2019

Language

English (en)

Author's ORCID

http://orcid.org/0000-0001-9404-7552

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Mathematics Commons

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