Uniform Convergence Rate ofEstimators of Autocovariances in Partly Linear Regression Modelswith Correlated Errors期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Uniform Convergence Rate ofEstimators of Autocovariances in Partly Linear Regression Modelswith Correlated Errors

Authors:	Jin-hong?You,Gemai?Chen author-information" > author-information__contact u-icon-before" > mailto:gchen@math.ucalgary.ca" title=" gchen@math.ucalgary.ca" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Min?Chen,Xue-lei?Jiang

Affiliation:	(1) University of Regina, Regina, Saskatchewan, S4S 0A2, Canada;(2) University of Calgary, Calgary, Alberta, T2N 1N4, Canada;(3) Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

Abstract:	Consider the partly linear regression model $y_{i} = {x}'_{i} beta + g{left( {t_{i} } right)} + varepsilon _{i} ,;;{kern 1pt} 1 leqslant i leqslant n$ , where y _i’s are responses, $x_{i} = {left( {x_{{i1}} ,x_{{i2}} , cdots ,x_{{ip}} } right)}^{prime } ;;;{text{and}};;;t_{i} in {cal T}$ are known and nonrandom design points, is a compact set in the real line , β = (β ₁, ··· , β _p)' is an unknown parameter vector, g(·) is an unknown function and {ε _i} is a linear process, i.e., $varepsilon _{i} {kern 1pt} = {kern 1pt} {sumlimits_{j = 0}^infty {psi _{j} e_{{i - j}} ,{kern 1pt} ;psi _{0} {kern 1pt} = {kern 1pt} 1,;{kern 1pt} {sumlimits_{j = 0}^infty {{left\| {psi _{j} } right\|} < infty } }} }$ , where e _j are i.i.d. random variables with zero mean and variance $sigma ^{2}_{e}$ . Drawing upon B-spline estimation of g(·) and least squares estimation of β, we construct estimators of the autocovariances of {ε _i}. 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 _i} 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. Supported by the Knowledge Innovation Project of Chinese Academy of Sciences (No. KZCX2-SW-118) and the National Natural Science Foundation of China (No. 70221001).

Keywords:	Uniform strong convergence rate autocovariance and autocorrelation B-spline estimation correlated error partly linear regression model.
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