Computer-intensive methods for nonparametric time series analysis'

该项目的重点是开发不依赖于不切实际或无法核实的模型假设的时间序列和随机场分析的推理方法。具体地说，研究人员和他的同事们正在研究：(A)将AR-Sieve Bootstrap的适用范围扩展到线性时间序列的设置之外；(B)设计一种新的时频Bootstrap过程，其中尽管重采样发生在频域，但Bootstrap伪序列是在时间域生成的；(C)设计一种具有更大重采样大小的剩余Bootstrap方案，用于改进从时间序列数据进行的密度估计；(D)构建一种自动高效聚集谱密度估计器的方法；(E)测试密度的支持性，以及测试过差和估计消失点的谱密度；(F)设计改进的块自举程序以处理周期性或几乎周期性相关的时间序列；(G)对局部平稳时间序列和不均匀(但局部均匀)的标记点过程进行重采样和推断；和(H)研究函数数据重新抽样的不同方面，包括适当地研究函数统计的困难问题。自从基本认识到计算机在现代统计学中的潜在作用以来，Bootstrap和其他计算机密集型统计方法得到了广泛的发展，用于用独立数据进行推断。在相依数据的情况下，这种方法甚至更加重要，因为估计量和检验统计量的分布理论可能很难获得或不切实际。此外，最近的信息爆炸导致了前所未有的数据集，这就需要灵活的、非参数的、计算机密集型的数据分析方法。时间序列分析在许多不同的科学学科中尤其重要，例如在经济学、工程学、声学、地质统计学、生物统计学、医学、生态学、林业、地震学和气象学中。由于该提案为相关数据的统计分析制定了高效和可靠的方法，因此可以从具有实际重要性的数据集中得出更准确和可靠的推论，从而为社会带来可观的好处。例如，来自气象学/大气科学的数据，如气候数据；经济学，如股市回报；医学，如脑电数据；生物信息学，如基因组数据。

The project focuses on the development of methods of inference for the analysis of time series and random fields that do not rely on unrealistic or unverifiable model assumptions. In particular, the investigator and his colleagues are working on: (a) extending the range of applicability of the AR-sieve bootstrap beyond the setting of linear time series; (b) devising a new Time-Frequency bootstrap procedure in which bootstrap pseudo-series are generated in the time domain although the resampling happens in the frequency domain; (c) devising a residual bootstrap scheme with larger resample size to be used for improved density estimation from time series data; (d) constructing an automatic method of efficient aggregation of spectral density estimators; (e) testing for the support of a density, as well as testing for overdifferencing and estimating the spectral density at a vanishing point; (f) devising an improved block bootstrap procedure to handle time series that are periodically or almost periodically correlated; (g) resampling and inference for locally stationary time series and inhomogeneous (but locally homogeneous) marked point processes; and (h) investigating different aspects of resampling with functional data, including the difficult problem of appropriately studentizing a functional statistic.Ever since the fundamental recognition of the potential role of the computer in modern statistics, the bootstrap and other computer-intensive statistical methods have been developed extensively for inference with independent data. Such methods are even more important in the context of dependent data where the distribution theory for estimators and tests statistics may be difficult or impractical to obtain. Furthermore, the recent information explosion has resulted in data sets of unprecedented size that call for flexible, nonparametric, computer-intensive methods of data analysis. Time series analysis in particular is vital in many diverse scientific disciplines, e.g., in economics, engineering, acoustics, geostatistics, biostatistics, medicine, ecology, forestry, seismology, and meteorology. As a consequence of the proposal's development of efficient and robust methods for the statistical analysis of dependent data, more accurate and reliable inferences may be drawn from data sets of practical import resulting into appreciable benefits to society. Examples include data from meteorology/atmospheric science, such as climate data, economics, such as stock market returns, medicine, such as EEG data, and bioinformatics, such as genomic data.