The Consistency for the Estimators of Semiparametric Regression Model with Dependent Samples  

作　　者：Yi WU Xue-jun WANG Ling CHEN Kun JIANG 

机构地区：[1]School of Big Data and Artificial Intelligence,Chizhou University,Chizhou 247000,China [2]School of Mathematical Sciences,Anhui University,Hefei 230601,China

出　　处：《Acta Mathematicae Applicatae Sinica》2021年第2期299-318,共20页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(11671012,11871072);the Natural Science Foundation of Anhui Province(1808085QA03,1908085QA01,1908085QA07);the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0003)。

摘　　要：For the semiparametric regression model:Y^((j))(x_(in),t_(in))=t_(in)β+g(x_(in))+e^((j))(x_(in)),1≤j≤k,1≤i≤n,where t_(in)∈R and x(in)∈Rpare known to be nonrandom,g is an unknown continuous function on a compact set A in R^(p),e^(j)(x_(in))are m-extended negatively dependent random errors with mean zero,Y^((j))(x_(in),t_(in))represent the j-th response variables which are observable at points xin,tin.In this paper,we study the strong consistency,complete consistency and r-th(r>1)mean consistency for the estimatorsβ_(k,n)and g__(k,n)ofβand g,respectively.The results obtained in this paper markedly improve and extend the corresponding ones for independent random variables,negatively associated random variables and other mixing random variables.Moreover,we carry out a numerical simulation for our main results.

关 键 词：semiparametric regression model strong consistency complete consistency mean consistency m-END random variables 

分 类 号：O212.1[理学—概率论与数理统计]