Nonparametric Methods for Functional Data

函数数据的非参数方法

• 批准号: 0505537
• 负责人: Hans-Georg Mueller
• 金额: $ 10.09万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505537&HistoricalAwards=false
• 关键词: Nonparametric; Methods; Functional; Data

The investigator will combine theoretical analysis and applied tools todevelop innovative models, methodology, algorithms and data analysis forfunctional data. A major goal of this proposal is to extend the reach offunctional data analysis methods to sparse, noisy and irregularly sampledlongitudinal data. Functional data and longitudinal data are assumed to begenerated by random trajectories that correspond to realizations of anunderlying stochastic process. These trajectories may be either observableor hidden. Relevant theory for estimation and inference will be developed.Current functional data analysis approaches and tools require denselymeasured functions or completely observed functions on a common domain,and abandoning these assumptions requires new tools. Similarly, extensionsof functional data analysis to situations where one has both longitudinaland survival time components will lead to new practical statisticalmethods as well as challenging research problems. The development andapplication of new tools for curve warping in cases where a large fractionof the variability of random curves lies in variation of time scale isanother challenging problem that will be addressed.The statistical methods that will be developed by the investigator aremotivated by the need to analyze data that include large samples of geneexpression profiles, longitudinal studies in medicine and biology withmultivariate or generalized measurements, and time courses of behavioralmeasurements, coupled with age-at-death information. It is expected thatthe results of the proposed research will contribute in a significant wayto the analysis and interpretation of such data and will lead to newinsights into underlying mechanisms of gene regulation, complex dynamicinteractions in biological systems, and aging and longevity.

研究人员将结合理论分析和应用工具，为功能数据开发创新的模型、方法、算法和数据分析。这一建议的一个主要目标是将函数数据分析方法的范围扩展到稀疏、有噪声和不规则采样的纵向数据。假设函数数据和纵向数据是由对应于潜在随机过程的实现的随机轨迹产生的。这些轨迹可能是可见的，也可能是隐藏的。当前的函数数据分析方法和工具需要公共域上的密度测量函数或完全观测函数，而放弃这些假设需要新的工具。类似地，将函数数据分析扩展到既有纵向分量又有生存时间分量的情况将导致新的实用统计方法以及具有挑战性的研究问题。在随机曲线的大部分变异性存在于时间尺度变化的情况下，开发和应用新的曲线弯曲工具是另一个将被解决的具有挑战性的问题。调查者将开发的统计方法的动机是需要分析数据，包括大样本的基因表达谱，多变量或广义测量的医学和生物学的纵向研究，以及行为测量的时间进程，以及死亡年龄信息。预计拟议的研究结果将对这些数据的分析和解释做出重大贡献，并将导致对基因调控、生物系统中复杂的动态相互作用以及衰老和寿命的潜在机制的新认识。