Estimation for single-index and partially linear single-index integrated models
研究了非平稳单指标和部分线性单指标模型的估计，用正交级数逼近未知链接函数，推导出估计量的双重和三重收敛速度，并建立新中心极限定理，蒙特卡洛模拟验证了理论结果。
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.