Efficient Estimation in Semiparametric Time Series Models

半参数时间序列模型的高效估计

• 批准号: 0072174
• 负责人: Anton Schick
• 金额: $ 8.4万
• 依托单位: SUNY at Binghamton
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2003-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072174&HistoricalAwards=false
• 关键词: Efficient; Estimation; Semiparametric; Time; Series

Semiparametric models play a major role in many fields and have been extensively studied over the last two decades. Great emphasis has been placed on models with independent (and identically) distributed observations and quite some progress has been made in this case. Models with dependent observations, however, been mainly neglected up to now from an efficiency point of view. The proposed research will tackle open issues in the construction of efficient estimates and tests in semiparametric models with an emphasis on models with dependent observations. Such models include stationary and ergodic Markov chains and other time series models which are plentiful in many fields such as econometrics and financial mathematics. Efficient estimation of the finite-dimensional component as well as aspects of the infinite-dimensional component will be addressed. The latter include innovation distributions in time series models, invariant distributions of ergodic Markov chains, and stationary distributions of several consecutive observations.The main emphasis of the proposed research will be to develop a methodology for the construction of efficient estimates in semiparametric models with dependent observations. In the process the proposed research will have to develop methods that deal with the difficulties associated with an efficient score function that cannot be calculated explicitly, a problem that is also of great interest for models with independent observations. Finally, the proposed research will continue the work of the principal investigator in semiparametric regression models with an emphasis on improving existing methods of constructing root-n consistent and efficient estimates.

半参数模型在许多领域发挥着重要作用，并且在过去二十年中得到了广泛的研究。人们非常重视具有独立（且相同）分布观测值的模型，并且在这种情况下已经取得了相当大的进展。 然而，从效率的角度来看，具有相关观测值的模型迄今为止主要被忽视。 拟议的研究将解决半参数模型中构建有效估计和测试的开放问题，重点是具有相关观测值的模型。 此类模型包括平稳和遍历马尔可夫链以及其他时间序列模型，这些模型在计量经济学和金融数学等许多领域中都很丰富。 将解决有限维分量以及无限维分量的各方面的有效估计。 后者包括时间序列模型中的创新分布、遍历马尔可夫链的不变分布以及多个连续观测值的平稳分布。拟议研究的主要重点将是开发一种在具有相关观测值的半参数模型中构建有效估计的方法。 在此过程中，所提出的研究必须开发出方法来解决与无法明确计算的有效得分函数相关的困难，这个问题对于具有独立观察的模型也很感兴趣。 最后，拟议的研究将继续主要研究者在半参数回归模型方面的工作，重点是改进构建根 n 一致且有效估计的现有方法。