Statistical inference in a panel data semiparametric regression model with serially correlated errors

Jinhong You, Xian Zhou*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider a panel data semiparametric partially linear regression model with an unknown vector β of regression coefficients, an unknown nonparametric function g(·) for nonlinear component, and unobservable serially correlated errors. The correlated errors are modeled by a vector autoregressive process which involves a constant intraclass correlation. Applying the pilot estimators of β and g(·), we construct estimators of the autoregressive coefficients, the intraclass correlation and the error variance, and investigate their asymptotic properties. Fitting the error structure results in a new semiparametric two-step estimator of β, which is shown to be asymptotically more efficient than the usual semiparametric least squares estimator in terms of asymptotic covariance matrix. Asymptotic normality of this new estimator is established, and a consistent estimator of its asymptotic covariance matrix is presented. Furthermore, a corresponding estimator of g(·) is also provided. These results can be used to make asymptotically efficient statistical inference. Some simulation studies are conducted to illustrate the finite sample performances of these proposed estimators.

Original languageEnglish
Pages (from-to)844-873
Number of pages30
JournalJournal of Multivariate Analysis
Volume97
Issue number4
DOIs
Publication statusPublished - Apr 2006
Externally publishedYes

Keywords

  • Asymptotic normality
  • Consistency
  • Intraclass correlation
  • Panel data
  • Partially linear regression model
  • Semiparametric estimation
  • Serially correlated errors

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