{"ID":6023605,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T14:11:27.630055639Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06330","arxiv_id":"2607.06330","title":"Direct and efficient estimation of bilinear forms in staggered tensor panels","abstract":"We study the estimation of bilinear forms from noisy, partially observed tensor 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 analyse 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, rather than completing the entire tensor. 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. 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 through experiments on both simulated and real-world datasets.","short_abstract":"We study the estimation of bilinear forms from noisy, partially observed tensor 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 inferen...","url_abs":"https://arxiv.org/abs/2607.06330","url_pdf":"https://arxiv.org/pdf/2607.06330v1","authors":"[\"Alberto Bordino\",\"Thomas B. Berrett\",\"Olga Klopp\"]","published":"2026-07-07T14:26:36Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}