On Single-Index Coefficient Regression Models
研究了一类依赖关系的单指数系数回归模型，该模型能避免多维非参数估计中的维数灾难，并自动选择阈值变量，提出了估计方法并证明了估计量的一致性和渐近正态性。
Abstract In this article we investigate a class of single-index coefficient regression models under dependence. This includes many existing models, such as the smooth transition threshold autoregressive (STAR) model of Chan and Tong, the functional-coefficient autoregressive (FAR) model of Chen and Tsay, and the single-index model of Ichimura. Compared to the varying-coefficient model of Hastie and Tibshirani, our model can avoid the curse of dimensionality in multivariate nonparametric estimations. Another advantage of this model is that a threshold variable is chosen automatically. An estimation method is proposed, and the corresponding estimators are shown to be consistent and asymptotically normal. Some simulations and applications are also reported.