非参数回归模型中误差方差的样条估计Spline Estimate of Error Variance in Nonparametric Regression Models
武新乾,张刚
摘要(Abstract)：
针对具有固定设计和混合相依误差的非参数回归模型,构造了误差方差的多项式样条估计,证明了估计量的相合性,并且通过模拟算例说明了估计方法的可行性.
关键词(KeyWords)： 非参数回归;误差方差;样条估计;混合;相合性
基金项目(Foundation): 国家自然科学基金资助项目,编号11326181;; 河南省国际科技合作计划项目,编号134300510034;; 河南科技大学博士科研启动基金资助项目,编号4010-13480008
作者(Author): 武新乾,张刚
参考文献(References)：
- [1]Robinson P M.Large-sample inference for nonparametric regression with dependent errors[J].The Annals of Statistics,1997,25(5):2054-2083.
- [2]Park C G,Kim I,Lee Y S.Error variance estimation via least squares for small sample nonparametric regression[J].Journal of Statistical Planning and Inference,2012,142(8):2369-2385.
- [3]Qiu D,Shao Q,Yang L.Efficient inference for autoregressive coefficients in the presence of trends[J].Journal of Multivariate Analysis,2013,114(2):40-53.
- [4]孙耀东,徐宝,赵志文.固定设计下时间序列非参数回归模型的方差变点检验[J].郑州大学学报:理学版,2014,46(1):1-4.
- [5]李佳,李永明.PA误差下的半参数回归模型估计的矩相合性[J].信阳师范学院学报:自然科学版,2013,26(1):23-26.
- [6]Burman P.Regression function estimation from dependent observations[J].Journal of Multivariate Analysis,1991,36(2):263-279.
- [7]Wahba G.Bayesian“confidence intervals”for the cross-validated smoothing spline[J].Journal of the Royal Statistical Society:Series B,1983,45(1):133-150.
- [8]Zhou S,Shen X,Wolfe D A.Local asymptotics for regression splines and confidence regions[J].The Annals of Statistics,1998,26(5):1760-1782.
- [9]Mao W,Zhao L H.Free-knot polynomial splines with confidence intervals[J].Journal of the Royal Statistical Society:Series B,2003,65(4):901-919.
- [10]武新乾.线性过程误差下回归函数的样条估计[J].河南科技大学学报:自然科学版,2010,31(5):94-97.
- [11]Tran L,Roussas G,Yakowitz S,et al.Fixed-design regression for linear time series[J].The Annals of Statistics,1996,24(3):975-991.