发表机构
Czech Technical University in Prague; Imperial College London（布拉格捷克理工大学; 帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究仅从重复横截面观测识别特殊半鞅的可预测漂移，提出双线性二次约束规划及空间分支定界法求解，并给出估计量速率分解。
AI 中文摘要
一个特殊半鞅允许唯一分解 $X=X_0+M+A$，其中 $M$ 是局部鞅，$A$ 是可预测的有限变差部分。我们考虑当 $X$ 仅通过重复横截面观测时的 $A$ 的识别问题。此时估计目标是采样的可预测补偿器到可观测特征滤波（即当前状态以及群体中共享的任何随机性）上的投影，因此在固定扩散系数下，边际流仅能识别漂移直至一个马尔可夫投影。如果漂移是观测滞后窗口的仿射泛函，则联合问题是一个凸二次规划，其解即计量经济学中的伪面板回归。我们主要关注的情况（我们认为此前未被处理过）是漂移为隐藏线性动力系统的输出，而该系统的动力学本身需从边际分布中识别。此时联合问题是一个双线性二次约束规划，我们通过空间分支定界法求解并保证全局最优性；在无惩罚的状态扰动和随网格增长的漂移基下，该问题在潜在维度为一时即为 NP 难（通过从 $\ell^1$ 秩一矩阵近似归约），而固定潜在维度下确定性系统的复杂度仍属开放问题。块坐标分解提供了一种更廉价的替代方案。对于估计量本身，我们在固定网格下获得了速率，并将其分解为蒙特卡洛、估计和网格贡献三部分。
英文摘要
A special semimartingale admits a unique decomposition $X=X_0+M+A$ into a local martingale $M$ and a predictable finite-variation part $A$. We consider the identification of $A$ when $X$ is observed only through repeated cross-sections. The estimand is then the projection of the sampled predictable compensator onto the observable feature filtration, namely the current state together with whatever randomness is shared across the population, so that at a fixed diffusion coefficient the marginal flow identifies the drift only up to a Markovian projection. If the drift is an affine functional of an observed lag window, the joint problem is a convex quadratic programme whose solution is the pseudo-panel regression of econometrics. Our principal concern is the case, which we believe not to have been treated before, in which the drift is the output of a hidden linear dynamical system whose dynamics are themselves to be identified from the marginals. The joint problem is then a bilinear quadratically constrained programme, which we solve to certified global optimality by spatial branch and bound; with unpenalised state disturbances and a drift basis growing with the grid it is NP-hard already in latent dimension one, by reduction from $\ell^1$ rank-one matrix approximation, whereas the complexity of the deterministic system at fixed latent dimension remains open. A block-coordinate decomposition offers a cheaper alternative. For the estimator itself, we obtain rates at a fixed mesh, separated into Monte-Carlo, estimation and grid contributions.
