Computer-Intensive Methods for Nonparametric Analysis of Dependent Data

自从认识到计算机在现代统计中的作用以来，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。这种方法在依赖数据的环境中更为重要，在这种环境中，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、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，包括经济学、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。本研究项目旨在发展有效和稳健的方法，对相关数据进行统计分析，使从具有实际意义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效益。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。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，研究者及其同事正在研究：(a)平稳随机场的马尔可夫型重采样和线性过程自举；(b)非齐次标记点过程推理的局部块自举；(c)估计平稳数据的共同密度的平滑度和支持度；(d)通过使用平顶核改进非参数估计；(e)时间序列“过差分”原假设的自举检验；(f)近周期数据的季节性块自举；(g)局部平稳时间序列的无模型点预测器和预测区间；(h)局部平稳多元时间序列时变协方差矩阵的光滑估计；(i)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。

Ever since the recognition of the 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, computer-intensive methods of data analysis. Time series analysis in particular is vital in many diverse scientific disciplines, including economics, engineering, acoustics, geostatistics, biostatistics, medicine, ecology, forestry, seismology, and meteorology. This research project aims to develop efficient and robust methods for the statistical analysis of dependent data that will enable more accurate and reliable inferences to 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). 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 colleagues are working on: (a) Markov-type resampling and linear process bootstrap for stationary random fields; (b) local block bootstrap for inference with inhomogeneous marked point processes; (c) estimation of the degree of smoothness and support of the common density of stationary data; (d) improved nonparametric estimation via the use of flat-top kernels; (e) a bootstrap test for the null hypothesis of time series "over-differencing;" (f) seasonal block bootstrap for almost-periodic data; (g) model-free point predictors and prediction intervals for locally stationary time series; (h) smooth estimation of time-varying covariance matrices for locally stationary multivariate time series; and (i) different aspects of resampling with functional data, including the difficult open problem of appropriately studentizing a functional statistic.