Nonparametric Methods for Functional Data

研究者将结合理论分析和应用工具来开发功能数据的创新模型、方法、算法和数据分析。本文的主要目标是将可达函数数据分析方法扩展到稀疏、噪声和不规则采样的纵向数据。假设功能数据和纵向数据是由随机轨迹生成的，这些轨迹对应于潜在随机过程的实现。这些轨迹可能是可观察到的，也可能是隐藏的。将发展相关的估计和推理理论。当前的功能数据分析方法和工具需要在公共域上密集测量的函数或完全观察到的函数，放弃这些假设需要新的工具。同样，将功能数据分析扩展到同时具有纵向和生存时间成分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。在随机曲线的很大一部分可变性在于时间尺度变化的情况下，开发和应用新的曲线翘曲工具是将解决的另一个具有挑战性的问题。研究者将开发的统计方法的动机是分析数据的需要，这些数据包括大样本的基因表达谱，医学和生物学的纵向研究，多变量或广义测量，行为测量的时间过程，以及死亡年龄信息。预计该研究的结果将对这些数据的分析和解释做出重大贡献，并将对基因调控的潜在机制、生物系统中复杂的动态相互作用以及衰老和长寿产生新的认识。

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.