TY - JOUR
T1 - Weighted denoised minimum distance estimation in a regression model with autocorrelated measurement errors
AU - You, Jinhong
AU - Zhou, Xian
AU - ZHU, Lixing
AU - Zhou, Bin
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/5
Y1 - 2011/5
N2 - This paper deals with the linear regression model with measurement errors in both response and covariates. The variables are observed with errors together with an auxiliary variable, such as time, and the errors in response are autocorrelated. We propose a weighted denoised minimum distance estimator (WDMDE) for the regression coefficients. The consistency, asymptotic normality, and strong convergence rate of the WDMDE are proved. Compared with the usual denoised least squares estimator (DLSE) in the previous literature, the WDMDE is asymptotically more efficient in the sense of having smaller variances. It also avoids undersmoothing the regressor functions over the auxiliary variable, so that data-driven optimal choice of the bandwidth can be used. Furthermore, we consider the fitting of the error structure, construct the estimators of the autocorrelation coefficients and the error variances, and derive their large-sample properties. Simulations are conducted to examine the finite sample performance of the proposed estimators, and an application of our methodology to analyze a set of real data is illustrated as well.
AB - This paper deals with the linear regression model with measurement errors in both response and covariates. The variables are observed with errors together with an auxiliary variable, such as time, and the errors in response are autocorrelated. We propose a weighted denoised minimum distance estimator (WDMDE) for the regression coefficients. The consistency, asymptotic normality, and strong convergence rate of the WDMDE are proved. Compared with the usual denoised least squares estimator (DLSE) in the previous literature, the WDMDE is asymptotically more efficient in the sense of having smaller variances. It also avoids undersmoothing the regressor functions over the auxiliary variable, so that data-driven optimal choice of the bandwidth can be used. Furthermore, we consider the fitting of the error structure, construct the estimators of the autocorrelation coefficients and the error variances, and derive their large-sample properties. Simulations are conducted to examine the finite sample performance of the proposed estimators, and an application of our methodology to analyze a set of real data is illustrated as well.
KW - Asymptotic normality
KW - Autoregressive process
KW - Auxiliary variable
KW - Denoised minimum distance estimation
KW - Measurement errors
UR - http://www.scopus.com/inward/record.url?scp=79955471120&partnerID=8YFLogxK
U2 - 10.1007/s00362-009-0227-7
DO - 10.1007/s00362-009-0227-7
M3 - Journal article
AN - SCOPUS:79955471120
SN - 0932-5026
VL - 52
SP - 263
EP - 286
JO - Statistical Papers
JF - Statistical Papers
IS - 2
ER -