Semiparametric estimation for partially linear models with ψ-weak dependent errors

Eunju Hwang, Dong Wan Shin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Semiparametric estimators are developed for a partially linear regression model with ψ-weakly dependent errors. The ψ-weak dependence condition, introduced by Doukhan and Louhich [Doukhan, P., and Louhich, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 84, 313-342], unifies weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The class of ψ-weak dependent processes includes many important nonlinear processes such as stationary threshold autoregressive processes and bilinear processes as well as stationary ARMA processes. Asymptotic normalities are established for semiparametric generalized least squares estimators of the parametric component and for estimators of the nonparametric function. Expansions are obtained for the biases and variances of the estimators. Real data set and simulated data set analyses are provided for a model with a threshold autoregressive error process.

Original languageEnglish
Pages (from-to)411-424
Number of pages14
JournalJournal of the Korean Statistical Society
Issue number4
StatePublished - Dec 2011

Bibliographical note

Funding Information:
The authors are very grateful for valuable comments of two anonymous referees and an associate editor. This work was supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827).


  • Asymptotic normality
  • Partially linear model
  • Primary
  • Secondary
  • Semiparametric generalized least squares estimator
  • Weak dependence


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