Computer-intensive methods for nonparametric time series analysis'

该项目侧重于开发用于分析时间序列和随机场的推理方法，这些方法不依赖于不切实际或无法验证的模型假设。特别是，研究者和他的同事们正在努力：(a)扩大ar筛自举法的适用范围，超出线性时间序列的设置；(b)设计一种新的时频自举过程，该过程中，重采样发生在频域，但在时域产生自举伪序列；(c)设计更大样本量的残差自举方案，以改进时间序列数据的密度估计；(d)构造一种谱密度估计量的自动高效聚合方法；(e)测试密度的支撑性，以及测试过差和估计消失点处的谱密度；(f)设计一种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理；(h)研究功能数据重采样的不同方面，包括适当研究功能统计量的难题。自从人们基本认识到计算机在现代统计中的潜在作用以来，自举法和其他计算机密集型统计方法得到了广泛的发展，用于独立数据的推断。在依赖数据的情况下，这种方法甚至更为重要，因为估计量和测试统计量的分布理论可能难以获得或不切实际。此外，最近的信息爆炸导致了空前规模的数据集，这需要灵活的、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。由于该建议发展了对相关数据进行统计分析的有效而有力的方法，可以从具有实际意义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/大气科学的数据，如气候数据；经济学，如股票市场回报；医学，如脑电图数据；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.