Jackknifing in partially linear regression models with serially correlated errors

Jinhong You*, Xian Zhou, Gemai Chen

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper jackknifing technique is examined for functions of the parametric component in a partially linear regression model with serially correlated errors. By deleting partial residuals a jackknife-type estimator is proposed. It is shown that the jackknife-type estimator and the usual semiparametric least-squares estimator (SLSE) are asymptotically equivalent. However, simulation shows that the former has smaller biases than the latter when the sample size is small or moderate. Moreover, since the errors are correlated, both the Tukey type and the delta type jackknife asymptotic variance estimators are not consistent. By introducing cross-product terms, a consistent estimator of the jackknife asymptotic variance is constructed and shown to be robust against heterogeneity of the error variances. In addition, simulation results show that confidence interval estimation based on the proposed jackknife estimator has better coverage probability than that based on the SLSE, even though the latter uses the information of the error structure, while the former does not.

Original languageEnglish
Pages (from-to)386-404
Number of pages19
JournalJournal of Multivariate Analysis
Volume92
Issue number2
DOIs
Publication statusPublished - Feb 2005
Externally publishedYes

Keywords

  • Asymptotic normality
  • Consistency
  • Jackknife-type estimation
  • Partially linear regression model
  • Robustness
  • Semiparametric least-squares estimator
  • Serially correlated errors

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