Abstract

Time-stamped data are increasingly central to modern statistical applications. Such data offer unique opportunities to understand dynamic behavior and to guide real-time decision-making. Meanwhile, this temporal richness leads to new methodological and theoretical challenges.
In the first part, I will discuss Euclidean embedding of the event history data through dynamic factor models and internal covariates. The approach enables dimension reduction and effective information borrowing across multiple counting processes. Identifiability and near minimax optimality are established.
The second part also deals with time-stamped data that naturally arise in sequential experiments where data collection itself can be adaptive. I will introduce how variance minimization problem can be formulated within an online convex optimization framework. The resulting adaptive design achieves adversarial minimax optimality while still permitting valid statistical inference. I conclude by briefly discussing extensions, including delayed responses and time-varying comparators.