Use of estimating functions to improve sequential adaptive decisions and dynamic regularization

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Inspired by my vision of developing innovative statistical theories and methods to a broad range of applications involving dynamic factors and uncertainty, my long term research program has been motivated by practical issues and impact arising from important socioeconomic needs including financial modeling, insurance risk management and complex health data analysis. Specifically my research interests include (I) statistically modeling adaptive decision processes for a variety of applications, (II) reducing data dimensionality and problem complexity, and statistically estimating the state and predicting the future movement of adaptive decision processes having unknown dynamics, (III) effectively balancing between exploitation (i.e., applying what appears to be the best among the decisions we have taken so far) and exploration (i.e., taking risk and trying a new decision) for the best global performance of the sequential adaptive decision process. Such adaptive decision processes are typically characterized with significant methodological challenges and practical constraints, including modelling dynamic data streams (e.g., time series models, state space models and filtering), adaptive but dynamic decisions (e.g., bandit models and Markov decision processes), complex data structures (such as of spatial and temporal, hyperspectral data), and randomness of the underlying environment (such as Markov switching). Aligned to my long term research goals, this NSERC proposal is focused on specific goals of enhancing statistical models and approaches such as regularization and generalized Bayesian estimating functions, with various applications such as risk management, algorithmic trading, insurance control, and reinforcement learning. I will build this NSERC program on my current research achievements on estimating functions and search for the interplay of the Bayesian and frequentist estimating functions for better state estimation, and better address the exploitation and exploration dilemma by incorporating the interplay into the bandit models, state space models and filtering, and complex models driven by stable noise with Markov switching. The proposed research program is important for training HQP on interdisciplinary research. In the next five years, I propose to train five undergraduate students, five M.Sc. students, and one Ph.D. student (to start September 2024). My research group currently has four M.Sc. students and one research assistant. The highly qualified personnel will be involved in all stages of the proposed research program and objectives. My group members and I anticipate high quality publications, conference presentations and interdisciplinary collaborations from the achieved research.