基于B-S样条下的半参数可加保序模型的性质  

Properties of Semi-parametric Additive Isotonic Regression Model Based on B-S Splines

作　　者：温美沙 王晓光[2] 刘晓洁 杨静 李珍珍 屈文欢 WEN Mei-sha;WANG Xiao-guang;LIU Xiao-jie;YANG Jing;LI Zhen-zhen;QU Wen-huan(Department of Statistics,School of Sciences,Hebei North University,Zhangjiakou,Hebei 075031,China;College of Mathematics,Dalian University of Technology,Dalian,Liaoning 116024,China)

机构地区：[1]河北北方学院理学院统计系,河北张家口075031 [2]大连理工大学数学科学学院,辽宁大连116024

出　　处：《河北北方学院学报（自然科学版）》2021年第7期1-6,13,共7页Journal of Hebei North University:Natural Science Edition

摘　　要：目的半参数保序回归模型有效地平衡了数据的灵活性和准确性,且经常应用于许多领域,如医药、经济、大数据等。方法介绍了半参数可加保序回归模型的性质。模型中每个可加非参函数是单调的,且这些单调函数被带有约束条件的Bernstein-Schoenberg样条来逼近。结果在这个模型中,每个可加函数被证明有一样的收敛速度,同时参数部分的系数估计量被证明√n是相合和渐近正态的。结论采用该方法能够很好地证明其性质成立。Objective Semi-parametric isotonic regression model effectively balances the flexibility and accuracy of data,which is often applied in many fields,such as medicine,economy,big data,etc.Methods This paper introduces the properties of the semi-parametric additive isotonic regression model where every additive nonparametric function is monotonic,and these monotonic functions are approximated by Bernstein-Schoenberg splines with isotonic constraint.Results The estimate of each additive functional component is proved to have the same convergence rate and the coefficient estimators of the parameter portion are square root of n congruent,which is asymptotically normal.Conclusion The method can be used to prove the validity of its properties.

关 键 词：半参数模型 可加模型 保序回归 样条 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]