【作者】 武新乾； 田铮； 田萍；

【Author】 WU Xin-qian, TIAN Zheng, TIAN Ping(Department of Applied Mathematics, Northwestern Polytechnical University, Xian710072; National Key Laboratory of Pattern Recognition, & Institute of Automation,Chinese Academy of Sciences, Beijing 100080; College of Applied Sciences, BeijingUniversity of Technology, Beijing 100022)

【机构】 西北工业大学应用数学系； 北京工业大学应用数理学院；

【摘要】 考虑一类部分线性自回归模型,其中,线性项中的解释变量为响应变量的滞后变量,未知非参数函数中的解释变量为一般随机变量。旨在利用多项式样条方法,对未知参数和非参数函数进行估计。在适当的条件下,给出了这些估计量的相合性和收敛速度。模拟算例不仅表明了该方法的可行性,而且建议使用BIC准则由数据追赶法自动选择结点个数。更多还原

【Abstract】 A partly linear autoregressive model, in which explanatory variables in linear component consist of some lagged values of response variable but an explanatory variable in unknown nonparametric function is a general random variable, is considered. The purpose is to estimate unknown parameters and nonparametric function using a polynomial spline method. Consistency and convergence rates of these estimators are given under some mild conditions. The methodology is illustrated by simulation and BIC criteria is suggested to use for automatically selecting knot number through a data-driven method.更多还原