Inference for Low-rank Completion without Sample Splitting with Application to Treatment Effect Estimation

TL;DR

This paper develops a novel inference method for low-rank matrix estimation that does not require sample splitting, applicable to dependent data, and demonstrates its use in treatment effect estimation.

Contribution

It introduces a sample-splitting-free inference approach for low-rank matrices, accommodating dependent observations and heterogeneous sampling.

Findings

Asymptotic normality of eigenvector estimators established

Method successfully applied to estimate treatment effects in a real-world case

No sample splitting needed, simplifying the inference process

Abstract

This paper studies the inferential theory for estimating low-rank matrices. It also provides an inference method for the average treatment effect as an application. We show that the least square estimation of eigenvectors following the nuclear norm penalization attains the asymptotic normality. The key contribution of our method is that it does not require sample splitting. In addition, this paper allows dependent observation patterns and heterogeneous observation probabilities. Empirically, we apply the proposed procedure to estimating the impact of the presidential vote on allocating the U.S. federal budget to the states.