Statistical Inference for Noisy Incomplete Binary Matrix
Authors: Yunxiao Chen, Chengcheng Li, Jing Ouyang, Gongjun Xu; Volume 24, Issue 95, Pages 1-66, 2023.
Abstract
This paper focuses on statistical inference for noisy incomplete binary (or 1-bit) matrices. While matrix completion is important for uncertainty quantification, most of the literature on categorical matrix completion primarily deals with point estimation and prediction. This paper takes a step further and addresses statistical inference for binary matrix completion. Using a popular nonlinear factor analysis model, we propose a point estimator and establish its asymptotic normality. Our analysis employs a flexible missing-entry design that does not require a random sampling scheme, unlike most of the existing asymptotic results for matrix completion. Under reasonable conditions, the proposed estimator is statistically efficient and achieves the Cramer-Rao lower bound asymptotically for the model parameters. We also present two applications: (1) linking two forms of an educational test and (2) linking roll call voting records from multiple years in the United States Senate. The first application allows for a comparison between examinees who took different test forms, while the second application enables a comparison of the liberal-conservativeness of senators who did not serve in the Senate at the same time.
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