随机缺失函数型时间序列数据的k近邻回归估计
|
摘要
针对响应变量随机缺失的强混合函数型时间序列数据,首次提出了非参数回归模型的k近邻估计,并在一些正则条件下建立了k近邻回归算子的几乎完全一致收敛速度.此研究不仅推进了函数型非参数模型的理论研究,也为函数型数据的实际应用领域提供了理论支撑.
We first investigate the k-nearest neighbours(kNN)estimation of nonparametric regression model for strongly mixing functional time series data with responses missing at random.We establish the uniform almost complete convergence rates of the kNN estimator under some regular conditions.Our research promotes the theoretical research of functional nonparametric regression model and provides theoretical support in functional data practical application field.
We first investigate the k-nearest neighbours(kNN)estimation of nonparametric regression model for strongly mixing functional time series data with responses missing at random.We establish the uniform almost complete convergence rates of the kNN estimator under some regular conditions.Our research promotes the theoretical research of functional nonparametric regression model and provides theoretical support in functional data practical application field.
引文
[1]Burba F,Ferraty F,Vieu P.k-Nearest Neighbour method in functional nonparametric regression[J].Journal of Nonparametric Statistics,2009,21(4):453-469.
[2]Biau G,Cérou F,Guyader A.Rate of convergence of the functional k-nearest neighbor estimate[J].IEEE Transactions on Information Theory,2010,56(4):2034-2040.
[3]Attouch M K,Benchikh T.Asymptotic distribution of robust k-nearest neighbour estimator for functional nonparametric models[J].Matematicki Vesnik,2012,64(4):275-285.
[4]Kudraszow N L,Vieu P.Uniform consistency of kNN regressors for functional variables[J].Statistics and Probability Letters,2013,83:1863-1870.
[5]Ferraty F,Vieu P.Nonparametric Functional Data Analysis[M].Berlin:Theory and Practice.Springer,2006.
[6]吴波.基于遍历函数型数据条件风险率函数的核估计[J].大学数学,2015,31(6):20-25.
[7]柏培鑫,凌能祥,金菊良.基于函数型非参数方法的气温数据预测分析[J].大学数学,2017,33(3):46-51.
[2]Biau G,Cérou F,Guyader A.Rate of convergence of the functional k-nearest neighbor estimate[J].IEEE Transactions on Information Theory,2010,56(4):2034-2040.
[3]Attouch M K,Benchikh T.Asymptotic distribution of robust k-nearest neighbour estimator for functional nonparametric models[J].Matematicki Vesnik,2012,64(4):275-285.
[4]Kudraszow N L,Vieu P.Uniform consistency of kNN regressors for functional variables[J].Statistics and Probability Letters,2013,83:1863-1870.
[5]Ferraty F,Vieu P.Nonparametric Functional Data Analysis[M].Berlin:Theory and Practice.Springer,2006.
[6]吴波.基于遍历函数型数据条件风险率函数的核估计[J].大学数学,2015,31(6):20-25.
[7]柏培鑫,凌能祥,金菊良.基于函数型非参数方法的气温数据预测分析[J].大学数学,2017,33(3):46-51.