The Consistency of LSE Estimators in Partial Linear Regression Models under Mixing Random Errors  

作　　者：Yun Bao YAO Yu Tan LÜ Chao LU Wei WANG Xue Jun WANG 

机构地区：[1]School of Mathematical Sciences,Anhui University,Hefei 230601,P.R.China [2]School of Big Data and Artificial Intelligence,Chizhou University,Chizhou 247000,P.R.China [3]School of Big Data and Statistics,Anhui University,Hefei 230601,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第5期1244-1272,共29页数学学报（英文版）

基　　金：Supported by the National Social Science Foundation of China(Grant No.22BTJ059)。

摘　　要：In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to be estimated,random errorsε_(i)are(α,β)-mix_(i)ng random variables.The p-th(p>1)mean consistency,strong consistency and complete consistency for least squares estimators ofβ^(*)and g(·)are investigated under some mild conditions.In addition,a numerical simulation is carried out to study the finite sample performance of the theoretical results.Finally,a real data analysis is provided to further verify the effect of the model.

关 键 词：(α β)-mixing random variables partial linear regression model least squares estimator CONSISTENCY 

分 类 号：O212.1[理学—概率论与数理统计]