Nonparametric Methods for Functional Data

研究者将联合收割机理论分析和应用工具相结合，开发创新的模型、方法、算法和功能数据的数据分析。这项建议的一个主要目标是将功能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。函数数据和纵向数据被假定为由随机轨迹产生，对应于一个潜在的随机过程的实现。这些轨迹可能是可观察的，也可能是隐藏的。目前的功能数据分析方法和工具需要在一个共同的域上密集测量的功能或完全观察的功能，放弃这些假设需要新的工具。同样，功能数据分析的扩展到同时具有生存时间和生存时间的情况，将导致新的实用的治疗方法以及具有挑战性的研究问题。另一个需要解决的挑战性问题是，在随机曲线的变异性很大程度上取决于时间尺度的变化的情况下，曲线弯曲的新工具的开发和应用。研究者将开发的统计方法的动机是分析数据的需要，包括大样本的基因表达谱，医学和生物学中的纵向研究与多变量或广义测量，和行为测量的时间过程，再加上死亡时的年龄信息。预计这项研究的结果将有助于对这些数据的分析和解释，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长寿的潜在机制的新认识。

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.