论文标题
一些有关随时间变化的非参数回归和局部固定回归器的理论结果和错误
Some Theoretical Results Concerning Time-varying Nonparametric Regression with Local Stationary Regressors and Error
论文作者
论文摘要
关于三步估计程序，提出了Li和您在应用统计和管理期刊中没有理论讨论的，对于具有时变回归函数的非参数回归模型，局部固定回归器和时间变化的AR（P）（TVAR（P））（TVAR（P））错误过程，我们为每个估算器的所有必要的渐近性属性。我们得出了非参数回归函数初步估计的收敛速率和渐近正态性，在错误项中建立了时间变化系数函数的渐近分布，并介绍了非参数回归函数的精制估计的渐近性能。此外，关于可变选择的Ulasso方法和错误术语结构的恒定系数检测，我们表明Ulasso估计器可以始终如一地识别真实的错误术语结构。我们进行了两项仿真研究，以说明估计量的有限样本性能，并验证我们对估计剂特性的理论讨论。
With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local stationary regressors and time-varying AR(p) (tvAR(p)) error process , we established all necessary asymptotic properties for each of estimator. We derive the convergence rate and asymptotic normality of the preliminary estimation of nonparametric regression function, establish the asymptotic distribution of time-varying coefficient functions in the error term, and present the asymptotic property of the refined estimation of nonparametric regression function. In addition, with regard to the ULASSO method for variable selection and constant coefficient detection for error term structure, we show that the ULASSO estimator can identify the true error term structure consistently. We conduct two simulation studies to illustrate the finite sample performance of the estimators and validate our theoretical discussion on the properties of the estimators.
