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都是至关重要的。该项目继续开发计算机密集的统计推断方法，以便在不依赖不切实际或无法核实的模型假设的情况下分析相关数据。具体地说：(A)一般估计量是基于收敛/发散统计的嵌套子样本值构造的，其一般应用包括尾部指数和速率估计。(B)证明了具有(可能)重尾的标记点过程的自归一化统计量的分布的极限定理；说明了在没有明确的重尾指数的情况下，如何使用次抽样来进行推断。(C)在剩余Bootstrap的背景下，以及在非参数自回归中的函数估计、条件矩估计、谱密度和大样本协方差矩阵估计中，都建议使用特殊的“平顶”核。(D)设计了两种不同的块自举方案，一种基于局部分块技术，另一种基于残差，以处理来自局部(但不是全局)平稳序列的数据。(E)确定了在线性/非线性(自动)回归模型中进行最强Bootstrap假设检验的方法，并作为结果设计了强大的Bootstrap单位根检验。本项目属于非参数统计领域，其中推断(估计、可信区间、假设检验等)。在不依赖于临时模型假设的情况下执行。在某种意义上，非参数观点允许数据“自己说话”，尤其适用于数据丰富的“大样本”情况；在我们的信息爆炸时代，这逐渐成为一种典型情况。例如，在跨越十年的每日汇率或股票回报序列中，或者在过去100年的(平均)年气温序列中，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未保持不变。这个项目的一部分涉及设计适当的计算机密集方法，用于在这种非平稳环境中进行推断(例如，趋势检测和估计)，这将对经济应用和气候变化问题最有帮助。作为另一个例子，考虑从全国各地的气象站收集的气象数据；由于测量的空间位置高度不规则，这种类型的数据构成了所谓的“标记点过程”。该项目下的工作为在这种实际重要和困难的情况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.