单指标和部分线性单指标综合模型的估计
Estimation for single-index and partially linear single-index integrated models
摘要：
本文主要研究了两类常用模型的估计问题：单指标模型和部分线性单指标模型。这类模型具有非平稳性。用正交级数展开来逼近模型中的未知可积连接函数，用剖面法来推导估计量。结果包括双收敛速率的单指标模型和三个收敛速度的部分线性单指标模型的估计。对未知连接函数的插入式估计量建立了一个新的中心极限定理。同时，在第四节中，我们还讨论了一类部分非线性单指标模型的推广。蒙特卡罗模拟验证了这些理论结果。一个实证研究阐明了所提出的估计程序在实践中的应用。
英文摘要：
Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index models. A new central limit theorem is established for a plug-in estimator of the unknown link function. Meanwhile, a considerable extension to a class of partially nonlinear single-index models is discussed in Section 4. Monte Carlo simulation verifies these theoretical results. An empirical study furnishes an application of the proposed estimation procedures in practice.
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