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

arXiv: https://arxiv.org/abs/2307.16370 · HTML: https://mlsanity.com/paper/2307.16370/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [CoreFlow: Low-Rank Matrix Generative Models](https://mlsanity.com/paper/2604.24959/) (2026)

## Abstract (arXiv)

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.