Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors  

作　　者：Jin-hongYou GemaiChen MinChen ue-leiJiang 

机构地区：[1]UniversityofRegina,Regina,Saskatchewan,S4S0A2,Canada [2]UniversityofCalgary,Calgary,Alberta,T2N1N4,Canada [3]AcademyofMathematicsandSystemSciences,ChineseAcademyofSciences,Beijing100080.China

出　　处：《Acta Mathematicae Applicatae Sinica》2003年第3期363-370,共8页应用数学学报（英文版）

基　　金：the Knowledge Innovation Project of Chinese Academy of Sciences (No.KZCX2-SW-118);the National Natural Science Foundation of China (No.70221001).

摘　　要：Consider the partly linear regression model , where y <SUB>i </SUB>’s are responses, are known and nonrandom design points, is a compact set in the real line , &#946; = (&#946; <SUB>1</SUB>, ··· , &#946; <SUB>p </SUB>)' is an unknown parameter vector, g(·) is an unknown function and {&#949; <SUB>i </SUB>} is a linear process, i.e., , where e <SUB>j </SUB>are i.i.d. random variables with zero mean and variance . Drawing upon B-spline estimation of g(·) and least squares estimation of &#946;, we construct estimators of the autocovariances of {&#949; <SUB>i </SUB>}. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {&#949; <SUB>i </SUB>} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process.Consider the partly linear regression model , where y <SUB>i </SUB>’s are responses, are known and nonrandom design points, is a compact set in the real line , &#946; = (&#946; <SUB>1</SUB>, ··· , &#946; <SUB>p </SUB>)' is an unknown parameter vector, g(·) is an unknown function and {&#949; <SUB>i </SUB>} is a linear process, i.e., , where e <SUB>j </SUB>are i.i.d. random variables with zero mean and variance . Drawing upon B-spline estimation of g(·) and least squares estimation of &#946;, we construct estimators of the autocovariances of {&#949; <SUB>i </SUB>}. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {&#949; <SUB>i </SUB>} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process.

关 键 词：Uniform strong convergence rate autocovariance and autocorrelation B-spline estimation correlated error partly linear regression model 

分 类 号：O212.1[理学—概率论与数理统计]