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是至关重要的。该项目继续发展计算机密集的统计推理方法，以分析相关数据，而不依赖于不现实或无法验证的模型假设。特别是：(a)一般估计量是基于收敛/发散统计量的嵌套子样本值构造的，一般应用包括尾指数和率估计。(b)证明了带有（可能）重尾的标记点过程的自归一化统计量分布的极限定理；它显示了如何在没有明确的知识和/或估计重尾指数的情况下将子抽样用于推理目的。(c)证明了在残差自举的背景下，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等问题中，都建议使用特殊的“平顶”核。(d)设计了两种不同的块引导方案，一种基于局部块技术，另一种基于残差，用于处理局部（而不是全局）平稳序列的数据。(e)确定了在线性/非线性（自）回归设置中进行最强大的自举假设检验的方法，并设计了强大的自举单位根检验。该项目属于非参数统计领域，其中推论（估计、置信区间、假设检验等）在不依赖于特别模型假设的情况下进行。在某种意义上，非参数观点允许数据“为自己说话”，并且特别适用于数据丰富的“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的情况。例如，在跨越十年的每日汇率序列或股票回报序列中，或者在过去100年的（平均）年温度序列中，可能有证据表明，该序列的随机结构在如此长的时间内并没有保持不变。这个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，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。再举一个例子，考虑从遍布全国的气象站收集的气象数据；由于测量的空间位置是高度不规则的，这种类型的数据构成了所谓的“标记点过程”。该项目的工作为在如此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.