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进行以下工作：(A)对多变量平稳时间序列的矩阵值自协方差序列的一致估计，以及即使在高维过程的背景下也有效的后续线性过程Bootstrap过程；(B)平顶核及其在改进的风险比率函数的非参数估计和谱密度估计器的聚集中的应用；(C)对概率密度的支持测试和对时间序列的过差的测试；(D)用于周期性或几乎周期性相关的时间序列的新的块Bootstrap过程；(E)在局部平稳时间序列的背景下的估计和检验以及对可能不齐次的标记点过程的重采样推断；(F)函数数据重采样的不同方面，包括适当地对函数统计进行学科化这一难题。自从从根本上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，以便用独立的数据进行推断。这种方法在相依数据的情况下更加重要，在这种情况下，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，这些数据集需要灵活的、非参数的、必要的计算机密集的数据分析方法。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。例子包括气象学/大气科学数据(如气候数据)、经济学数据(如股市回报)、生物统计学数据(如功能磁共振成像数据)和生物信息学数据(如遗传学和微阵列数据)。

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).