An orthogonal series estimate of time-varying regression

  • Wŀodzimierz Greblicki
  • Danuta Rutkowska
  • Leszek Rutkowski


Let (X 1,Y 1), (X 2,Y 2),... be independent pairs of random variables according to the modelY n =t n (X n )R(X n )+Z n ,n=1,2,..., wheret n andR are unknown functions.Z n 's are i.i.d. random variables with zero mean and finite variance. The marginal density ofX n is independent ofn. In the paper nonparametric estimates of a nonstationary regression function E{Y n |X n =x}=t n (x)R(x) are proposed and their asymptotic properties are investigated.

Key words and phrases

Nonparametrio estimation regression function nonstationary regression function orthogonal series stochastic approximation 


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Copyright information

© Kluwer Academic Publishers 1983

Authors and Affiliations

  • Wŀodzimierz Greblicki
    • 1
    • 2
    • 3
  • Danuta Rutkowska
    • 1
    • 2
    • 3
  • Leszek Rutkowski
    • 1
    • 2
    • 3
  1. 1.Technical University of WrocŀawWrocŀawPoland
  2. 2.Technical University of CzęstochowaCzęstochowaPoland
  3. 3.Technical University of CzęstochowaCzęstochowaPoland

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