Efficient Estimation in Semiparametric Time Series Models

半参数模型在许多领域发挥着重要作用，在过去的二十年中得到了广泛的研究。重点放在具有独立（和相同）分布观测值的模型上，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，具有依赖观测值的模型迄今主要被忽视。提出的研究将解决半参数模型中有效估计和检验的构建中的开放问题，重点是具有依赖观测的模型。这些模型包括平稳马尔可夫链和遍历马尔可夫链等时间序列模型，这些模型在计量经济学和金融数学等许多领域都有大量应用。有限维分量的有效估计以及无限维分量的各个方面将被解决。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和若干连续观测的平稳分布。所提议的研究的主要重点将是开发一种方法，用于在具有依赖观测值的半参数模型中构建有效的估计。在此过程中，提出的研究将不得不开发方法来处理与无法明确计算的有效分数函数相关的困难，这一问题对于具有独立观测值的模型也是非常感兴趣的。最后，建议的研究将继续首席研究员在半参数回归模型方面的工作，重点是改进现有的构建根n一致和有效估计的方法。

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.