Statistical Inference with Missing and Latent Data: Methods for Data Harmonization, Network Curvature Estimation and Experimentation Under Interference

Abstract

This dissertation explores several statistical challenges involving inference problems where the object of interest is a latent phenomenon or involves missing data. Effective modeling of the latent processes or missing data is crucial for accurate inference in such scenarios. We delve into issues of missing and latent data across three distinct settings. The first project addresses missing outcomes resulting from changes in neuropsychological test battery versions, where each version represents different testing models and scales. The second project focuses on inference for causal parameters using partially measured network data, also highlighting the experimental design challenges associated with such problems. The final project presents a nonparametric method for estimating network curvature from distance matrices. This approach emphasizes network models and introduces tests for constant curvature, providing a clearer understanding of the underlying network structure.