Computer-intensive methods for nonparametric time series analysis'

该项目的重点是发展不依赖于不现实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。特别是，研究者和他的同事们正在努力：（a）将AR-筛子自助的适用范围扩展到线性时间序列的设置之外;（B）设计一种新的时频自助过程，其中自助伪序列在时域中产生，尽管恢复发生在频域中;（c）设计一个具有较大重采样尺寸的残差自助方案，用于改进从时间序列数据进行的密度估计;（d）构建一个自动有效聚合谱密度估计量的方法;（e）测试密度的支持，以及测试过差和估计 消失点的谱密度;（f）设计一个改进的块引导程序来处理周期性或几乎周期性相关的时间序列;（g）局部平稳时间序列和非齐次（但局部齐次）标记点过程的重采样和推断;以及（h）研究重采样的不同方面 函数数据，包括 自从人们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已经被广泛开发用于独立数据的推断。 这种方法在依赖数据的上下文中甚至更加重要 其中估计量和检验统计量的分布理论可能难以获得或不切实际。 此外，最近的信息爆炸 数据集的规模空前，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，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。 由于该提案为从属数据的统计分析制定了有效和可靠的方法， 可以从实际重要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利益。 例子包括来自气象学/大气科学的数据，如气候数据，经济学，如股市回报，医学，如EEG数据，以及生物信息学，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.