Local Linear Estimation of a Nonparametric Cointegration Model
研究了非平稳I(1)回归变量下非参数回归模型的局部线性估计量，推导了回归函数及其导数的联合渐近结果，并通过模拟验证了其相比局部常数估计量的效率优势。
The nonparametric local linear method has superior properties compared with the local constant method in the independent and weak dependent data setting, see e.g. Fan and Gijbels (1996 Fan , J. , Gijbels , I. ( 1996 ). Local Polynomial Modeling and Its Applications . London : Chapman and Hall/CRC . [Google Scholar]). Recently, much attention has been drawn to the nonparametric models with nonstationary data. Wang and Phillips (2009a) studied the asymptotic property of a local constant estimator of a nonparametric regression model with a nonstationary I(1) regressor. Sun and Li (2011 Sun , Y. , Li , Q. ( 2011 ). Data-driven bandwidth selection for nonstationary semiparametric models . Journal of Business and Economic Statistics 29 : 541 – 551 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) show a surprising result that for a semiparamtric varying coefficient model with nonstationary I(1) regressors, the local linear estimator has a faster rate of convergence than the local constant estimator. In this article, we study the asymptotic behavior of the local linear estimator for the same nonparametric regression model as considered by Wang and Phillips (2009a). We focus on the derivation of the joint asymptotic result of both the unknown regression function and its derivative function. We also examine the performance of the local linear estimator with the bandwidth selected by the data driven least squares cross validation (LS-CV) method. Simulation results show that the local linear estimator, coupled with the LS-CV selected bandwidth, enjoys substantial efficiency gains over the local constant estimator.