Estimation of Linear Functionals in Multilayer Panels under Staggered Adoption
Abstract
We study the estimation of bilinear forms from noisy, partially observed multilayer data. The signal follows a Tucker2 model, with shared unit and time factors across tensor layers and slice-specific cores. The missingness pattern is structured and motivated by staggered adoption designs, which are common in causal inference and related applications. We first analyze the four-block missingness pattern, the basic building block for general staggered adoption, and propose a spectral algorithm that pools information across layers and targets the functional directly. We prove a non-asymptotic mean squared error bound that exhibits a phase transition in the number of layers, showing when pooling improves estimation, and match it with a local minimax lower bound up to constants when ranks and logarithmic factors are treated as constant-order quantities. We then extend the construction to general staggered adoption designs via an anchored four-block reduction, and derive analogous theoretical guarantees. Finally, we validate our theoretical findings using synthetic and real-world data on Castle Doctrine laws and COVID-19 policies
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BibTeX
@misc{bordino2026estimation,
title = {{Estimation of Linear Functionals in Multilayer Panels under Staggered Adoption}},
author = {Alberto Bordino and Thomas B. Berrett and Olga Klopp},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.06330},
eprint = {2607.06330},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.06330},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Estimation of Linear Functionals in Multilayer Panels under Staggered Adoption
AU - Alberto Bordino
AU - Thomas B. Berrett
AU - Olga Klopp
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2607.06330
UR - https://arxiv.org/abs/2607.06330
AB - We study the estimation of bilinear forms from noisy, partially observed multilayer data. The signal follows a Tucker2 model, with shared unit and time factors across tensor layers and slice-specific cores. The missingness pattern is structured and motivated by staggered adoption designs, which are common in causal inference and related applications. We first analyze the four-block missingness pattern, the basic building block for general staggered adoption, and propose a spectral algorithm that pools information across layers and targets the functional directly. We prove a non-asymptotic mean squared error bound that exhibits a phase transition in the number of layers, showing when pooling improves estimation, and match it with a local minimax lower bound up to constants when ranks and logarithmic factors are treated as constant-order quantities. We then extend the construction to general staggered adoption designs via an anchored four-block reduction, and derive analogous theoretical guarantees. Finally, we validate our theoretical findings using synthetic and real-world data on Castle Doctrine laws and COVID-19 policies
ER -