arXiv 4 May 2026 · Statistics — Methodology
arXiv:2605.03204 · PDF · DOI · OpenAlex · Extracted main text
Peer effect estimation requires precise network measurement, yet most empirical networks are noisy, rendering standard estimators inconsistent. To address measurement error in networks, we propose a method to estimate peer effects in networks whose expected adjacency matrix is low-rank. Our key result shows that peer effects over a true unobserved network are asymptotically equivalent to peer effects over the expected adjacency matrix. This result reduces peer effect estimation in noisy networks to low-rank matrix estimation targeting the expected adjacency matrix. We develop our theory for weighted networks observed with additive noise, but simulations suggest approach can be applied more generally when there is a low-rank estimation method suited to a particular noise structure. We demonstrate via simulations that our approach applies to egocentric samples, aggregated relational data, and networks with missing edges, each requiring a different low-rank estimation method.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hayes, Alex, Levin, Keith (2025) Minimax Rates for the Linear-in-Means Model Reveal an Identifiability-Estimability Gap self | 1.000 | 6 | 3 | 100% |
| 2 | Kelejian, Harry H, Prucha, Ingmar R (1998) A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Distur… | 0.737 | 3 | 3 | 67% |
| 3 | Athreya, Avanti, Fishkind, Donniell E, Tang, Minh, Priebe, Carey E,… (2018) Statistical Inference on Random Dot Product Graphs: A Survey self | 0.737 | 3 | 2 | 100% |
| 4 | Leung, Michael P (2022) Causal Inference Under Approximate Neighborhood Interference | 0.737 | 3 | 2 | 100% |
| 5 | McFowland, Edward, Shalizi, Cosma Rohilla (2021) Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations | 0.737 | 3 | 2 | 100% |
| 6 | Hayes, Alex, Fredrickson, Mark M, Levin, Keith (2025) Estimating Network-Mediated Causal Effects via Principal Components Network Regression self | 0.693 | 9 | 3 | 33% |
| 7 | Levin, Keith, Lodhia, Asad, Levina, Elizaveta (2022) Recovering Shared Structure from Multiple Networks with Unknown Edge Distributions self | 0.659 | 7 | 3 | 29% |
| 8 | Bramoullé, Yann, Djebbari, Habiba, Fortin, Bernard (2009) Identification of Peer Effects through Social Networks | 0.644 | 2 | 2 | 100% |
| 9 | Lee, Lung-Fei (2002) Consistency and Efficiency of Least Squares Estimation for Mixed Regressive, Spatial Autoregressive Models | 0.644 | 2 | 2 | 100% |
| 10 | Lee, Lung-Fei (2003) Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 74 scored citations.