Computer-Intensive Methods for Nonparametric Analysis of Dependent Data

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、必然需要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好处。例如来自气象学/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，该项目侧重于开发不依赖于不切实际或无法核实的模型假设的相关数据的推断方法。特别是，主要研究人员和他的合作者将在以下方面工作：(A)大数据的二次采样和重采样，包括高维多变量时间序列的Bootstrap；(B)p，q均为大的ARMA(p，q)模型的新模型拟合和重采样；(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器；(D)具有(几乎)周期分量的时间序列的重采样；(E)平稳和非平稳数据的无模型Bootstrap；(F)估计平稳数据的光滑度和对公共密度的支持；(G)改进了对危险率函数的非参数估计；(H)“过度差异”零假设的自举检验；(I)平稳随机场的马尔可夫重采样和线性过程自举；以及(J)函数和高维时间序列的重采样的不同方面。

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.