Mathematical Sciences: Optimal Inference in Non-Linear Regression Models with Long Range Dependent Errors and in Non-Linear Time Series

数学科学：具有长程相关误差的非线性回归模型和非线性时间序列中的最优推理

• 批准号: 9402904
• 负责人: Hira Koul
• 金额: $ 10.5万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9402904&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Optimal; Inference; Non

A discrete time stationary stochastic process is said to be long range dependent if its correlations decrease to zero like a power of the lag, as the lag tends to infinity, but their sum diverges. Part I of the proposal proposes to investigate the large sample behavior of three classes of robust estimators and to develop asymptotically efficient and adaptive estimators in non-linear regression models when the errors are long range dependent with possibly unknown joint distributions. The Part II of the proposal is concerned with studying the asymptotic behavior of several classes of robust estimators and devloping asymptoticlaly optimal inference procedures in non-linear time series in the presence of regression component, in a semi-parametric setup. In particular, the P.I. plans to develop asymptotically efficient and adaptive estimators in random coefficient and threshold autoregression models when there may be a regression variable present in these models, in a llinear or non-linear fashion, and when the distributions of the random coefficient and the error variable are unknown. The optimal estimators would be developed a l a Hajek - Le Cam theory. A data set where an association between distant observations is slowly decaying but persistent, as distance between observations increases, is called long range dependent. Such data arise often in astronomy, economics, geophysics, hydrology, meteorology, and many other disciplines. An example worth mentioning is the data of 289 high-precision measurements on the 1-kg check standard weight made between 1963 to 1975 by the U.S. National Bureau of Standards. In spite of ideal conditions for preserving independence, the observations turned out to be long range dependent. The first part of the proposal is concerned with developing some optimal statistical procedures for analyzing the long range dependent data in the presence of a covariate. The second part of the proposal is concerned with developing efficient inferential procedures in some complicated time series models that often arise in econometrics. It is anticipated that these procedures will be broadly applicable and not very sensitive to model departures.

如果滞后倾向于无穷大，则据说离散的时间固定随机过程被认为长度取​​决于其相关性，但其总和差异。 该提案的第一部分提议研究三类稳健估计器的大样本行为，并在非线性回归模型中开发渐近效率和适应性估计量，当误差依赖于远距离的关节分布可能是未知的。该提案的第二部分涉及在半参数设置中研究非线性时间序列中的几类稳健估计量的渐近行为以及在非线性时间序列中的最佳推理过程的渐近行为。特别是P.I.当这些模型中可能存在回归变量时，以llinear或非线性方式以及随机系数的分布和错误变量的分布尚不清楚时，计划在随机系数和阈值自动估计模型中开发渐近效率和适应性估计器的计划尚不清楚。最佳估计器将被开发为Hajek -Le Cam理论。 一个数据集，其中遥远观测之间的关联正在缓慢衰减，但随着观测之间的距离的增加，持续存在称为远距离依赖性。这种数据通常是在天文学，经济学，地球物理学，水文学，气象学和许多其他学科中产生的。值得一提的一个例子是关于美国国家标准局在1963年至1975年之间的1公斤检查标准权重的289个高精度测量数据的数据。尽管保留独立性的理想条件，但事实证明这一点取决于远距离。该提案的第一部分涉及开发一些最佳统计程序，以分析协变量存在的远距离依赖数据。该提案的第二部分涉及在某些复杂的时间序列模型中开发有效的推论程序，这些模型经常在计量经济学中出现。可以预料，这些程序将广泛适用，并且对模型出发的敏感不是很敏感。