Computer-intensive methods for nonparametric time series analysis

时间序列和随机场的统计分析在许多不同的科学学科中至关重要。该项目继续开发计算机密集型统计推断方法，用于分析相关数据，而不依赖不切实际或无法核实的模型假设。特别是：（a）一般估计量是根据收敛/发散统计量的嵌套子样本值构造的，一般应用包括尾部指数和速率估计。(b)极限定理证明了标记点过程（可能）重尾的自归一化统计分布，它示出了如何子采样可以用于推理的目的，没有明确的知识和/或估计的重尾指数。(c)它表明，使用特殊的“平顶”内核的建议，无论是在背景下的残余自助，以及在非参数自回归，条件矩估计，谱密度和大样本协方差矩阵估计的功能估计的问题。(d)两种不同的块引导方案，一个基于局部块技术和其他的残差，设计来解决本地（但不是全球）平稳序列的数据。(e)在线性/非线性（自）回归设置中进行最强大的bootstrap假设检验的方法被确定，并且作为结果设计了强大的bootstrap单位根检验。该项目福尔斯非参数统计领域，其中推断（估计，置信区间，假设检验等）。在不依赖于特设模型假设的情况下进行。从某种意义上说，非参数观点允许数据“为自己说话”，特别适合于数据丰富的“大样本”情况;在我们这个信息爆炸的时代，这逐渐成为一种典型情况。例如，在一个跨越十年的每日汇率或股票收益序列中，或者在过去100年的一系列（平均）年温度中，可能有证据表明该序列的随机结构在如此长的时间段内并没有保持不变。该项目的一部分涉及设计适当的计算机密集型方法，用于在这种非平稳环境中进行推理（例如，另一个例子是，考虑从分散在全国各地的气象站收集的气象数据;由于测量的空间位置非常不规则，这类数据构成了所谓的“标记点过程”。该项目下的工作为在如此实际重要和困难的背景下分析数据提供了强有力的方法。

The statistical analysis of time series and random fields is vital in many diverse scientific disciplines. This project continues the development of computer-intensive statistical methods of inference for the analysis of dependent data without relying on unrealistic or unverifiable model assumptions. In particular: (a) General estimators are constructed based on nested subsample values of converging/diverging statistics with general applications including tail index and rate estimation. (b) Limit theorems are proven for the distribution of self-normalized statistics from marked point processes with (possibly) heavy tails; it is shown how subsampling can be used for inference purposes without explicit knowledge and/or estimation of the heavy tail index. (c) It is demonstrated that the use of special `flat-top' kernels is advised both in the context of residual bootstrap, as well as in the problems of functional estimation in nonparametric autoregression, estimation of conditional moments, and spectral density and large-sample covariance matrix estimation. (d) Two different block bootstrap schemes, one based on a local blocking technique and the other on residuals, are devised to address data from locally (but not globally) stationary series. (e) The way to conduct a most powerful bootstrap hypothesis test in linear/nonlinear (auto)regression set-ups is identified and powerful bootstrap unit root tests are devised as a result.This project falls in the realm of nonparametric statistics where inferences (estimation, confidence intervals, hypothesis tests, etc.) are carried out without relying on ad hoc model assumptions. In some sense, the nonparametric viewpoint allows the data to ``speak for itself'', and is particularly appropriate in a `large-sample' situation where data are abundant; in our information-explosion age, this is progressively a typical situation. For example, in a daily series of exchange rates or stock returns spanning a decade, or a series of (average) annual temperatures over the last 100 years, there may be evidence that the stochastic structure of the series has not remained invariant over such a long stretch of time. Part of this project deals with devising appropriate computer-intensive methods for inference in such nonstationary environments (e.g., trend detection and estimation) that would be most helpful in economic applications as well as the problem of climate change.As another example, consider meteorological data gathered from weather stations scattered all around the country; since the spatial locations of the measurements are highly irregular, this type of data constitutes a so-called `marked point process'. The work under this project provides powerful methodology for the analysis of data under such practically important and difficult settings.