王青蓉.含自回归误差项的函数型线性模型的参数估计[J].重庆工商大学学报(自然科学版),2020,37(3):47-51
WANG Qing-rong.Parameter Estimation of Functional Linear Models with Autoregressive Error Term[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2020,37(3):47-51
含自回归误差项的函数型线性模型的参数估计
Parameter Estimation of Functional Linear Models with Autoregressive Error Term
  
DOI:
中文关键词:  函数型数据  函数主成分  自回归误差  收敛速度
英文关键词:functional data  functional principal component  autoregressive error  convergence speed
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作者单位
王青蓉 重庆工商大学 数学与统计学院,重庆 400067 
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中文摘要:
      针对模型误差为独立同分布的假设并不总是合适的,讨论含有自回归误差项的函数型线性回归模型。考虑到函数型变量和斜率函数无限维的特点,首先进行函数型主成分分析,以函数型变量的协方差函数作谱分解得到的特征函数为基函数,分别以该组基对函数型变量和斜率函数进行逼近,将无限维的参数转化为有限维基函数系数;然后构造AR(1)误差下函数型线性回归模型的参数估计,在一定条件下获得了与独立同分布场合下类似的结果;此外在均方误差的意义下,与忽略AR(1)误差项所得估计量相比,取得更小的均方误差,推广了现有文献中的一些结论和性质。
英文摘要:
      According to the fact that it is not always appropriate to assume that the model error is an independent isomorphic distribution, this paper discusses functional linear regression model with autoregressive error term. Considering the infinite dimensionality of functional variables and slope function, at first, this paper makes functional principal component analysis by taking the covariance function of functional variables as spectrum decomposition to obtain the basis function of characteristic function, then approximates the functional variables and the slope function by using this group basis respectively, so the parameters of infinite dimension are converted into basis function coefficients of finite dimension, and then constructs the parameter estimation of functional linear regression model with autoregressive error. Under certain condition, the result similar to independent isomorphic distribution is obtained. In addition, in the sense of mean square error, compared with the estimator of first order autoregressive error term, a smaller mean square error is received, which extends some conclusions and properties in the existing literatures.
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