Theory and Applications of Sharp Nonparametric Estimation and Learning

摘要PI：SAM EFROMOVICH提案编号：0243606本研究的主要重点是开发数据驱动的统计估计和学习的一般方法，并在环境，医学和生物应用中进行测试。 主要的智力目标有三个方面：（A）在已知尖锐渐近的情况下（如删失或有偏数据集），发展锐最优性的开始理论和小数据集统计模型之间的等价性;（B）在具有间接观测和滋扰函数的模型的情况下（如异方差非参数回归中的误差密度估计或时间序列中隐分量的恢复），发展了锐估计和定精度抽样理论;（C）在具有未知算子的逆问题的情况下，开发数据驱动的学习机器，这意味着尖锐的估计。实际问题包括塞维利亚国家野生动物保护区植物时空结构的统计建模、阿尔伯克基流域砷浓度的建模、城市污水处理厂的研究、汉坦病毒传播的统计建模以及用于恢复磁共振图像的学习机。本研究的主要重点是开发，与桑迪亚国家实验室和新墨西哥大学医学院合作，自适应统计估计和学习的算法和软件由以下环境，医学和生物应用激发并测试：塞维利亚国家野生动物保护区植物时空结构的统计建模;阿尔伯克基流域砷浓度的建模;城市污水处理厂的研究;汉坦病毒传播的统计建模;磁共振图像恢复的学习机。 研究的更广泛的影响是由很好理解的应用程序，可以鼓励学生学习数学，可以帮助更广泛的受众了解统计的重要性。 其影响是基于以下活动：㈠通过墨西哥国立大学的网络方案，开发一门关于适应性统计估计的新课程; ㈡每周科学研讨会㈢在新墨西哥大学瓦伦西亚校区举办的外联研讨会上定期发表演讲，以扩大代表性不足群体的参与; ㈣在调查员的网页上张贴开发的软件、数据库和可能引起更广泛受众兴趣的实际调查结果; ㈣在非技术性期刊上发表有益于社会的医学、环境和生物学调查结果。

abstractPI: SAM EFROMOVICHproposal number: 0243606The primary focus of this research is to develop general methods of data-driven statistical estimation and learning motivated by and tested on environmental, medical and biological applications. The main intellectual objectives are threefold:(A) In the case of settings with known sharp asymptotics (like censored or biased datasets), develop the theory of the onset of the sharp optimality and the equivalence between statistical models for small datasets; (B) In the case of models with indirect observations and nuisance functions (like error density estimation in heteroscedastic nonparametric regression or recovery of a hidden component in time series), develop the theory of sharp estimation and sampling with fixed accuracy; (C) In the case of inverse problems with unknown operator, develop data-driven learning machines implying sharp estimation. Practical problems include statistical modeling of temporal and spatial structures of plants in Sevilleta National Wildlife Refuge, modeling of arsenic concentration in Albuquerque water basin, the study of municipal wastewater treatment plants, statistical modeling of spreading hantavirus, and learning machines for recovery magnetic resonance images.The primary focus of this research is to develop, in collaboration with Sandia National Laboratories and the UNM Medical School, algorithms and software for adaptive statistical estimation and learning motivated by and tested on the following environmental, medical and biological applications: Statistical modeling of temporal and spatial structures of plants in Sevilleta National Wildlife Refuge; Modeling of arsenic concentration in Albuquerque water basin; Study of municipal wastewater treatment plants; Statistical modeling of spreading hantavirus; Learning machines for recovery magnetic resonance images. The broader impact of the research is defined by the well-understood applications that can encourage students to study mathematics and can help a broader audience to understand the importance of statistics. The impact is based on the following activities:(i) Developing a new course on adaptive statistical estimation taught via the UNM web-based program;(ii) Weekly scientific seminars (supported in part by private grants) held for undergraduate and graduate students, and talks during the UNM mathematical awareness weeks for high-school students;(iii) Regular presentations at outreach seminars conducted by the UNM Valencia campus to broaden participation of under-represented groups;(iv) Posting the developed software, databases, and practical findings, that can be of interest to a broader audience, on the investigator's webpage;(iv) Publishing of medical, environmental and biological findings, benefiting the society, in non-technical journals.