Asymptotic theory for partly linear models

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Abstract

Consider the model Yi= xiβ + g(ti) + Vi, 1≤ i ≤n. Here xi= (xil,…,xip) and tiare known and nonrandom design points, β = (βl,…,βp) is an unknown parameter, g(·) is an unknown function over R1, and Viis a class of linear processes. Based on g(·) estimated by nonparametric kernel estimation or approximated by a finite series expansion, the asymptotic normalities and the strong consistencies of the LS estimator of β and an estimator of σ 2 0= EV2 1are investigated.

Original languageEnglish
Pages (from-to)1985-2009
Number of pages25
JournalCommunications in Statistics - Theory and Methods
Volume24
Issue number8
DOIs
Publication statusPublished - 1 Jan 1995
Externally publishedYes

Keywords

  • Asymptotic normality
  • Linear process
  • Partly linear model
  • Strong convergence

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