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

• 作者: Yi WU Xue-jun WANG Ling CHEN Kun JIANG
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 299-318
• 页数: 20页
• 语种: 英文

摘要

For the semiparametric regression model: Y(j)(xin,tin) =tinβ+g(xin)+e(j)(xin),1 ≤j ≤ k,1 ≤i ≤ n,where tin ∈ R and xin ∈ Rp are known to be nonrandom,g is an unknown continuous function on a compact set A in Rp,ej (xin) are m-extended negatively dependent random errors with mean zero,Y(j)(xin,tin)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 estimators βk,n and gk,n of β and 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.