Computer-Intensive Methods for Nonparametric Analysis of Dependent Data

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，并在必要时，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。 例子包括气象学/大气科学（如气候数据）、经济学（如股票市场收益）、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。特别是，主要研究者及其合作者将致力于：（a）大数据的子采样和重新建模，包括大维度多变量时间序列的自举;（B）p，q都很大的阿尔马（p，q）模型的新模型拟合和重新建模;（c）局部平稳多变量时间序列的时变协方差矩阵的新平滑估计;（d）具有（几乎）周期成分的时间序列的恢复;（e）固定和非固定数据的无模型自举;（f）估计固定数据的平滑程度和共同密度的支持;（g）改进风险率函数的非参数估计;（h）“过度差异”零假设的自助检验;和（j）重新安置功能性和高级别残疾人的不同方面，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响进行评估，被认为值得支持审查标准。

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 into 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).The project focuses on the development of methods of inference for the analysis of dependent data that do not rely on unrealistic or unverifiable model assumptions. In particular, the principal investigator and his collaborators will work on: (a) Subsampling and resampling for Big Data, including bootstrap for multivariatetime series of large dimension; (b) New model fitting and resampling for ARMA (p,q) models with both p,q large; (c) New smoothing estimators of time-varying covariance matrices for locally stationary multivariate time series; (d) Resampling for time series with an (almost) periodic component; (e) Model-free Bootstrap for stationary and non-stationary data; (f) Estimating the degree of smoothness and support of the common density of stationary data; (g) Improved nonparametric estimation of a hazard rate function; (h) A bootstrap test for the null hypothesis of `overdifferencing'; (i) Markov-type resampling and Linear Process Bootstrap for stationary random fields; and (j) Different aspects of resampling of functional and high-dimensional time series.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.