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An Introduction to Best Empirical Models when the Parameter Space is Infinite Dimensional

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  • Werner Ploberger
  • Peter C. B. Phillips

Abstract

Ploberger and Phillips (Econometrica, Vol. 71, pp. 627–673, 2003) proved a result that provides a bound on how close a fitted empirical model can get to the true model when the model is represented by a parameterized probability measure on a finite dimensional parameter space. The present note extends that result to cases where the parameter space is infinite dimensional. The results have implications for model choice in infinite dimensional problems and highlight some of the difficulties, including technical difficulties, presented by models of infinite dimension. Some implications for forecasting are considered and some applications are given, including the empirically relevant case of vector autoregression (VAR) models of infinite order.

Suggested Citation

  • Werner Ploberger & Peter C. B. Phillips, 2003. "An Introduction to Best Empirical Models when the Parameter Space is Infinite Dimensional," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 877-890, December.
    • Handle: RePEc:bla:obuest:v:65:y:2003:i:s1:p:877-890
    DOI: 10.1046/j.0305-9049.2003.00089.x
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    Cited by:

    1. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.

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