Computer-intensive methods for nonparametric time series analysis

非参数时间序列分析的计算机密集型方法

• 批准号: 1308319
• 负责人: Dimitris Politis
• 金额: $ 24万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1308319&HistoricalAwards=false
• 关键词: Computer; intensive; methods; nonparametric; time

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).

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助程序，即使在高维过程的背景下也是有效的;（B）平顶核及其应用于改进的风险率函数的非参数估计和谱密度估计的聚集;（c）检验概率密度的支持和检验时间序列的过差;（d）周期性或几乎周期性相关的时间序列的新的块自举程序;（e）局部平稳时间序列的估计和检验以及可能非齐次标记点过程的恢复推断;以及（f）与函数数据相关的不同方面，包括如何适当地将函数统计学学生化的难题。 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已被广泛开发用于独立数据的推断。这种方法在相关数据的背景下更重要，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，最近的信息爆炸导致数据集的规模空前，需要灵活的，非参数的，而且-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。 由于该提案制定了对相关数据进行统计分析的有效和可靠的方法，因此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（例如气候数据）、经济学（例如股票市场回报）、生物统计学（例如功能性磁共振成像数据）和生物信息学（例如遗传学和微阵列数据）的数据。