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

我的愿景是开发创新的统计理论和方法，以广泛的应用，涉及动态因素和不确定性的启发，我的长期研究计划一直受到实际问题和重要的社会经济需求，包括金融建模，保险风险管理和复杂的健康数据分析所产生的影响的激励。具体来说，我的研究兴趣包括（I）统计建模各种应用程序的自适应决策过程，（II）减少数据维度和问题的复杂性，并统计估计状态和预测具有未知动态的自适应决策过程的未来运动，（III）有效地平衡剥削（即，应用我们迄今为止所采取的决定中看起来最好的）和探索（即，冒险并尝试新的决策），以获得顺序自适应决策过程的最佳全局性能。这种自适应决策过程通常具有显著的方法学挑战和实际约束的特征，包括对动态数据流（例如，时间序列模型、状态空间模型和滤波），自适应但动态的决策（例如，强盗模型和马尔可夫决策过程）、复杂的数据结构（例如空间和时间的、高光谱数据）和底层环境的随机性（例如马尔可夫切换）。与我的长期研究目标相一致，NSERC的这一提案侧重于增强统计模型和方法的具体目标，如正则化和广义贝叶斯估计函数，以及风险管理、算法交易、保险控制和强化学习等各种应用。我将建立这个NSERC程序在我目前的研究成果估计功能和搜索的贝叶斯和频率估计功能的相互作用，以更好的状态估计，并更好地解决开发和勘探困境，通过将相互作用纳入到强盗模型，状态空间模型和过滤，以及复杂的模型驱动的稳定噪声与马尔可夫切换。该研究计划对培养HQP进行跨学科研究具有重要意义。在未来五年内，我计划培养五名本科生，五名硕士生和一名博士生。学生（2024年9月开始）。我的研究小组目前有四名硕士生和一名研究助理。高素质的人员将参与拟议研究计划和目标的所有阶段。我和我的小组成员期待高质量的出版物，会议报告和跨学科合作，从所取得的研究。

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.