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研究：(a)多元平稳时间序列的矩阵值自协方差序列的一致估计，以及随后的线性过程自举程序，即使在高维过程的背景下也是有效的；(b)平顶核及其在改进危险率函数的非参数估计和谱密度估计集合中的应用；(c)概率密度的支持度检验和时间序列的过差分检验；(d)针对周期性或几乎周期性相关的时间序列，提出一种新的块自举程序；(e)局部平稳时间序列的估计和测试，以及对可能非齐次标记点过程的重采样推断；(f)功能数据重采样的不同方面，包括适当研究功能统计的困难开放问题。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、必要的、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有效和可靠的统计分析的方法，可以从具有实际意义的数据集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（如气候数据）、经济学（如股票市场回报）、生物统计学（如功能磁共振成像数据）和生物信息学（如遗传学和微阵列数据）的数据。

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) consistent estimation of the matrix-valued autocovariance sequence of a multivariate stationary time series, and a subsequent linear process bootstrap procedure that is valid even in the context of high-dimensional processes; (b) flat-top kernels and their application to improved nonparametric estimation of a hazard rate function and to aggregation of spectral density estimators; (c) testing for the support of a probability density and testing for over-differencing of a time series; (d) a new block bootstrap procedure for time series that are periodically or almost periodically correlated; (e) estimation and testing in the context of locally stationary time series and resampling inference for possibly inhomogeneous marked point processes; and (f) different aspects of resampling with functional data, including the difficult open 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 test statistics may be difficult or impractical to obtain. Furthermore, the recent information explosion has resulted in datasets of unprecedented size that call for flexible, nonparametric, and--by necessity--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 datasets of practical import resulting in appreciable benefits to society. Examples include data from meteorology/atmospheric science (e.g. climate data), economics (e.g. stock market returns), biostatistics (e.g. fMRI data), and bioinformatics (e.g. genetics and microarray data).