Convergence rates of estimators in partial linear regression models with MA(∞) error process

Xiaoqian Sun, Jinhong You, Gemai Chen, Xian Zhou*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


This paper is concerned with a partial linear regression model with serially correlated random errors which are unobservable and modeled by a moving-average process of infinite order. We study a class of estimators for the linear regression coefficients as well as the function characterizing the non-linear part of the model, constructed based on general kernel smoothing and least squares methods. The law of iterated logarithm and strong convergence rates of these estimator are derived by truncating the moving-average error process, a procedure widely applied in the analysis of time series. Our results can be used to establish uniform strong convergence rate of the estimators of autocovariance and autocorrelation functions of the error process.

Original languageEnglish
Pages (from-to)2251-2273
Number of pages23
JournalCommunications in Statistics - Theory and Methods
Issue number12
Publication statusPublished - 2002
Externally publishedYes


  • Linear time series errors
  • Nonparametric kernel smoothing
  • Partial linear regression model
  • Semiparametric least squares estimator
  • Strong convergence rates


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