{"ID":2859633,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.06524","arxiv_id":"2510.06524","title":"Stable central limit theorems for discrete-time lag martingale difference arrays","abstract":"Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain lagged filtrations but not given the natural filtration. We formalize this class of stochastic processes and prove a stable central limit theorem (CLT) via a Bernstein blocking scheme and an application of the classical martingale CLT. We generalize our limit theorem to vector-valued processes via the Cramér-Wold device and develop a simple form for the limiting variance. We demonstrate the application of these results to a problem in dynamic causal inference and present a simulation study supporting their validity.","short_abstract":"Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain lagged filtrations but not given the natural filtration. We formalize this clas...","url_abs":"https://arxiv.org/abs/2510.06524","url_pdf":"https://arxiv.org/pdf/2510.06524v2","authors":"[\"Walter Dempsey\",\"Easton Huch\"]","published":"2025-10-07T23:51:53Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}