Stable central limit theorems for discrete-time lag martingale difference arrays
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914179336634368 |
|---|---|
| author | Dempsey, Walter Huch, Easton |
| author_facet | Dempsey, Walter Huch, Easton |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable central limit theorems for discrete-time lag martingale difference arrays Dempsey, Walter Huch, Easton Statistics Theory Probability 60G48, 60F05 (Primary), 60G42, 60B12 (Secondary) 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. |
| title | Stable central limit theorems for discrete-time lag martingale difference arrays |
| topic | Statistics Theory Probability 60G48, 60F05 (Primary), 60G42, 60B12 (Secondary) |
| url | https://arxiv.org/abs/2510.06524 |