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 , β = (β <SUB>1<...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 , β = (β <SUB>1</SUB>, ··· , β <SUB>p </SUB>)' is an unknown parameter vector, g(·) is an unknown function and {ε <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 β, we construct estimators of the autocovariances of {ε <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 {ε <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.展开更多
基金the Knowledge Innovation Project of Chinese Academy of Sciences (No.KZCX2-SW-118)the National Natural Science Foundation of China (No.70221001).
文摘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 , β = (β <SUB>1</SUB>, ··· , β <SUB>p </SUB>)' is an unknown parameter vector, g(·) is an unknown function and {ε <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 β, we construct estimators of the autocovariances of {ε <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 {ε <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.
