Optimal statistical exploration and exploitation: theory, methods and applications

目前统计工作面临的挑战为推进统计理论和方法提供了机会，其特点是复杂的道德、理论和方法问题。在许多涉及不确定性的实际应用中，统计学习和即时预期收益之间的最佳平衡对于一系列决策的最佳整体性能是可取的。例如，在临床试验中平衡集体伦理（探索）和个人伦理（利用），以及在投资组合优化中高即时回报（利用）和低回报变异性（探索）。类似地，我们在统计推断中看到了偏差与方差的权衡，在统计建模中看到了拟合与复杂性的权衡。 我的长期研究计划专注于寻找重要和创新的统计理论和方法，以解决这些权衡和实际的社会经济需求，该提案具体集中在两个主题上。主题一的重点是开发和应用新的惩罚回归方法，同时收缩和变量选择，以解决适合与复杂性的权衡。这些方法是多重共线性和高维数据建模的核心。主题二着重于处理探索与开发的权衡，介绍新的协变量调整的反应自适应随机化程序，系统地研究其理论和方法问题，研究最优投资组合选择问题，并介绍新的动态风险度量。 希望本研究能对HQP的目标应用和HQP培训产生重要的影响。 惩罚回归用于分析基因表达数据，响应自适应设计正在成为绝望医疗情况下临床研究的新标准，动态风险度量对于金融机构确保金融稳定非常重要。该研究积极参与HQP具有明确的目标和方法，培训他们有效的（独立和协作）研究技能，沟通和职业技能，并在其研究领域建立坚实的统计理论和方法背景。

Current challenges to statistics, which offer opportunities for advancing statistical theory and methods, are characterized by complex ethical, theoretical and methodological issues. In many practical applications involving uncertainty, an optimal balance between statistical learning and immediate expected payoff is desirable for the best overall performance of a sequence of decisions. Examples include balancing the collective ethics (exploration) and individual ethics (exploitation) in clinical trials, and high immediate returns (exploitation) and low variability of returns (exploration) in portfolio optimization. Similarly we see the bias-versus-variance tradeoff in statistical inference and fit-versus-complexity tradeoff in statistical modeling. Contributing to my long term research programs that focus on searching for significant and innovative statistical theory and methods to address these tradeoffs and practical socio-economic needs, the proposal specifically centers on two main themes. Theme one focuses on developing and applying new methods of penalized regression for simultaneous shrinkage and variable selection to address the fit-versus-complexity tradeoff. Such methods are at the heart of multicollinearity and high dimensional data modeling. Theme two focuses on dealing with the exploration-versus-exploitation tradeoff, introducing new covariate adjusted response adaptive randomization procedures, systematically examining their theoretical and methodological issues, investigating problems of optimal portfolio selection and introducing new dynamic risk measures. The research is expected to have significant impact on the targeted applications and HQP training. Penalized regression is useful for analyzing gene expression data, response adaptive designs are becoming the new standard for clinical research in desperate medical situations, and dynamic risk measures are important for financial institutions to ensure financial stability. The research actively involves HQPs with clear objectives and methods, trains them effective (independent and collaborative) research skills, communication and career skills, and builds solid background on statistical theory and methodologies in their research fields.