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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (3): 265-274.doi: 10.3969/j.issn.1005-3085.2019.03.003

• • 上一篇    下一篇

相依误差下异方差非参数回归模型的样条估计

武新乾,  程   芳,  徐   珍   

  1. 河南科技大学数学与统计学院，洛阳  471023
  • 收稿日期:2017-03-20 接受日期:2017-06-30 出版日期:2019-06-15 发布日期:2019-08-15
  • 基金资助:
    国家自然科学基金(11501167; 11601126)；河南省重点攻关项目(182102210286).

Spline Estimation for Heteroscedastic Nonparametric Regression Models under Dependent Errors

WU Xin-qian,  CHENG Fang,  XU Zhen   

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023
  • Received:2017-03-20 Accepted:2017-06-30 Online:2019-06-15 Published:2019-08-15
  • Supported by:
    The National Natural Science Foundation of China (11501167; 11601126); the Key Program for Science and Technology Development of Henan Province (182102210286).

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摘要： 一些经济金融等实际数据中含有非线性趋势、异方差和相依关系，固定设计和相依误差下的异方差非参数回归模型因其能够反映这些数据特征而有着重要的应用．样条方法是常用的非参数光滑方法之一．为了探究样条方法在这类模型中的可用性，本文在$\alpha$- 混合条件下，讨论了均值函数和方差函数的多项式样条估计的逐点相合性，得到了逐点收敛速度．此外，还对所讨论的方法进行了数值模拟，结果表明样条方法在这类模型的应用中是可行的．

关键词: 非参数回归模型, 样条估计, 相合性, 收敛速度

Abstract: These exist non-linear trends, heteroscedasticity and dependent relations in some economic and financial data. The heteroscedastic non-parametric regression models with fixed design and dependent errors have been used in these fields because of its ability to reflect these data characteristics. The spline method is one of the commonly used non-parametric smoothing methods. In order to explore the application of the spline method to this kind of models, we discuss the pointwise consistency of polynomial spline estimators of the mean function and variance function under the $\alpha$-mixing condition, and obtain the pointwise rate of convergence. In addition, we carry out the numerical simulation, and the results show that the proposed spline method is feasible.

Key words: nonparametric regression models, spline estimation, consistency, rate of convergence

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