Efficient Estimation in Semiparametric Time Series Models

半参数模型在许多领域中发挥着重要作用，在过去的二十年中得到了广泛的研究。具有独立（同）分布观测值的模型一直是研究的重点，并取得了一定的进展。 然而，从效率的角度来看，具有相关观测值的模型到目前为止主要被忽视。 拟议的研究将解决开放的问题，在建设有效的估计和检验的半参数模型与依赖的观测模型的重点。 这些模型包括平稳和遍历马尔可夫链以及其他时间序列模型，在计量经济学和金融数学等许多领域都很丰富。 有限维分量的有效估计以及无限维分量的各个方面将得到解决。 后者包括时间序列模型中的新息分布、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，本文的主要研究重点将是发展一种方法来构造具有相依观测值的半参数模型的有效估计。 在这个过程中，拟议的研究将不得不开发的方法，处理与一个有效的分数函数，不能明确计算，一个问题，也是非常感兴趣的模型与独立的观察相关的困难。 最后，拟议中的研究将继续在半参数回归模型的主要研究者的工作，重点是改善现有的方法，构建根N一致和有效的估计。

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.