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Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data

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  • Dennis Kristensen

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

The main uniform convergence results of Hansen (2008) are generalized in two directions: Data is allowed to (i) be heterogenously dependent and (ii) depend on a (possibly unbounded) parameter. These results are useful in semiparametric estimation problems involving time-inhomogenous models and/or sampling of continuous-time processes. The usefulness of these results are demonstrated by two applications: Kernel regression estimation of a time-varying AR(1) model , and the kernel density estimation of a Markov chain that has not been intialized at its stationary distribution.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-37.

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Length: 13
Date of creation: 01 Jul 2008
Date of revision:
Handle: RePEc:aah:create:2008-37

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Nonparametric estimation; uniform consistency; kernel estimation; density estimation; heterogeneous time series;

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  1. Fermanian, Jean-David & Salani , Bernard, 2004. "A Nonparametric Simulated Maximum Likelihood Estimation Method," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 20(04), pages 701-734, August.
  2. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(03), pages 726-748, June.
  3. Rodríguez Poo, Juan M. & Ferreira García, María Eva & Orbe Mandaluniz, Susan, 2001. "Nonparametric estimation of time varying parameters under shape restrictions," BILTOKI, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística) 2001-02, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
  4. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 76-94.
  5. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 26(01), pages 60-93, February.
  6. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-59, School of Economics and Management, University of Aarhus.
  7. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, Elsevier, vol. 136(1), pages 163-188, January.
  8. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 241-283, January.
  9. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(03), pages 560-586, June.
  10. Li, Qi & Wooldridge, Jeffrey M., 2002. "Semiparametric Estimation Of Partially Linear Models For Dependent Data With Generated Regressors," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(03), pages 625-645, June.
  11. R. Dahlhaus & M. Neumann & R. von Sachs, 1997. "Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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