CAREER: Asymptotic Statistical Decision Theory and Its Applications

渐近等价理论是Lucien Le Cam在统计学上的重要贡献之一，它是一种将各种统计模型联系起来的理论。如果两个模型是渐近等价的，则所有渐近最优统计估计量都可以从一个模型转移到另一个模型。 建立渐近等价的一个基本原则是用一个更易处理的模型来近似一个复杂的统计模型。高斯位置模型是一个易于处理的模型，它捕捉了许多统计设置的本质。 调查研究明确和实用的程序转换为一般的非参数估计高斯回归，使用改进的分位数耦合不等式和新的方差稳定化变换。其他统计问题通过与泊松过程模型相联系可以更好地理解。研究了密度估计的无限可分近似及其与非参数边缘估计和分类的关系。研究者还建议研究该领域的一个长期存在的问题-无界损失的渐近等价理论，并研究多重比较，功能数据分析和长记忆模型的渐近等价理论。该项目将帮助许多领域的统计学家，如稳健的非参数估计、机器学习、多重比较、功能数据分析、长记忆模型和广义线性模型，理解和欣赏Le Cam理论的简化，并将其用作产生新理论和方法的指导。研究人员正在研究的模型可用于信号和图像处理，呼叫数据分析，生物武器使用检测，基因组研究，疾病预防等。该项目将通过教授决策理论课程，组织研讨会和讲习班来传播和保存Le Cam的理论，并为研究生提供建议，从而整合研究和教育。调查员将担任耶鲁统计系研究生招生的多样性协调员，并将寻求吸引妇女和少数民族对赠款进行研究。

Asymptotic equivalence, one of the most important statistical contributions of Lucien Le Cam, is a theory to build the connections among various statistical models. If two models are asymptotically equivalent, all asymptotically optimal statistical estimators can be carried over from one model to the other. A basic principle of establishing asymptotic equivalence is to approximate a complicated statistical model by a more tractable one. The Gaussian location model is a tractable model that captures the essence of a number of statistical settings. The investigator studies explicit and practical procedures to convert a general nonparametric estimation to a Gaussian regression, using improved quantile coupling inequalities and new variance stabilization transformations. Other statistical problems are better understood by relating them to Poisson process models. The investigator studies infinitely divisible approximation to density estimation and its connection to nonparametric edge estimation and classification. The investigator is also proposed to study a long-standing issue in this area -- asymptotic equivalence theory for unbounded loss, and to study the asymptotic equivalence theory for multiple comparisons, functional data analysis and long memory models. The project would help statisticians in many areas such as robust nonparametric estimation, machine learning, multiple comparison, functional data analysis, long memory models and generalized linear models, to understand and appreciate the simplification of Le Cam's theory and use it as a guidance to produce new theory and methodologies. The models the investigator is studying can be used in signal and image processing, calling data analysis, detection of bioweapons use, Genomic research, disease prevention, etc. The project will integrate research and education by teaching courses on decision theory, by organizing seminars and workshops to disseminate and preserve Le Cam's theory, and by advising graduate students working on this topic. The investigator will serve as the Diversity Coordinator for graduate student admissions in the Yale Statistics Department, and will seek to attract women and minorities to do research on the grant.