Online

Zhu, Damin

Mathematics and Statistics

2023

Ph. D.

This dissertation consists of two studies. The first develops theory for a new method for estimating regression parameters using generalized estimating equations (GEE) with panel data prone to covariate measurement error. The focus is on logistic regression, though the method is applicable to other models. The method requires availability ofinstrumental variables (IV) to identify model parameters. Simulations are performed to assess the performance of the proposed estimator. The method, abbreviated GEEIV, is able to accurately estimate logistic regression parameters masked by measurement error in a variety of population configurations. In the second study, an algorithm is proposed to estimate the number of latent defective edges in large hypergraphs. The new statistical method combines the strength of sampling strategies and an existing algorithmic method known for efficient latent edge identification for small graphs. Our statistical approach strikes a balance between computational time consumption and estimation power, with the flexibility to adapt to several assumption violations. Simulations are performed on both synthetic data and a simulator loaded with US western grid structures. The new algorithm was able give unbiased estimates using relatively little computational time for the synthetic data for a wide range of combinations of graph sizes, defective graph edges and defective edge distributions. Simulation results from US western grid data agreed with a previous study on relatively small latent edge sets. On a large edge set, previous studies were not able to provide a reasonable estimate. The new algorithm was able to give estimates and confidence intervals for the larger problem.