不确定半参数模型的Bernstein多项式估计  

Uncertain Semiparametric Model with Bernstein Polynomials

作　　者：丁建华[1,2] 张红玉 张志强 DING Jianhua;ZHANG Hongyu;ZHANG Zhiqiang(Department of Statistics,Shanxi Datong University,Datong,037009,China;KLATASDS-MOE,Shanghai,200062,China)

机构地区：[1]山西大同大学统计系,大同037009 [2]统计与数据科学前沿理论及应用教育部重点实验室,上海200062

出　　处：《应用概率统计》2022年第2期303-315,共13页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Statistical Science Research Project(Grant No.2020LY010);the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE,ECNU;the Fundamental Research Funds for the Central Universities.

摘　　要：假设样本观测值是不精确的,通过将不精确的观测值建模为不确定变量,这篇论文提出单调半参数模型的不确定统计推断.单调Bernstein多项式近似非参数函数,利用二次规划算法进行求解.并通过数值例子说明所提出的方法.Assuming the observations are imprecise and modeling the observations by uncertain variables,this paper proposes statistical inferences for uncertain semiparametric regression model when nonparametric function is subject to monotonicity constraint.Monotonic Bernstein polyno-mials are used to approximate the nonparametric function and quadratic programming algorithm is used to compute the estimate.A numerical example is given to illustrate the proposed methods.

关 键 词：不确定变量 不确定半参数模型 BERNSTEIN多项式 交叉证实法 

分 类 号：O212.7[理学—概率论与数理统计]