Weighted denoised minimum distance estimation in a regression model with autocorrelated measurement errors

Jinhong You*, Xian Zhou, Lixing ZHU, Bin Zhou

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)263-286
Number of pages24
JournalStatistical Papers
Issue number2
Publication statusPublished - May 2011

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Asymptotic normality
  • Autoregressive process
  • Auxiliary variable
  • Denoised minimum distance estimation
  • Measurement errors


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