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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

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 25 (2009)
Issue (Month): 05 (October)
Pages: 1433-1445

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Handle: RePEc:cup:etheor:v:25:y:2009:i:05:p:1433-1445_09

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Find related papers by JEL classification:

• C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
• C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models

References

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1. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
2. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
3. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
   
   • Dennis Kristensen & Yongseok Shin, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-58, School of Economics and Management, University of Aarhus.
4. Fermanian, Jean-David & Salani , Bernard, 2004. "A Nonparametric Simulated Maximum Likelihood Estimation Method," Econometric Theory, Cambridge University Press, vol. 20(04), pages 701-734, August.
5. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(01), pages 60-93, February.
   
   • Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus.
6. Li, Qi & Wooldridge, Jeffrey M., 2002. "Semiparametric Estimation Of Partially Linear Models For Dependent Data With Generated Regressors," Econometric Theory, Cambridge University Press, vol. 18(03), pages 625-645, June.
7. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
   
   • Federico M. Bandi & Peter C.B. Phillips, 2001. "Fully Nonparametric Estimation of Scalar Diffusion Models," Cowles Foundation Discussion Papers 1332, Cowles Foundation for Research in Economics, Yale University.
8. Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2005. "Nonparametric estimation of time varying parameters under shape restrictions," Journal of Econometrics, Elsevier, vol. 126(1), pages 53-77, May.
   
   • Rodríguez Poo, Juan M. & Ferreira García, María Eva & Orbe Mandaluniz, Susan, 2001. "Nonparametric estimation of time varying parameters under shape restrictions," BILTOKI 2001-02, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
9. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, School of Economics and Management, University of Aarhus.
10. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.

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Citations

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Cited by:

1. Dennis Kristensen & Andrew Ang, 2009. "Testing Conditional Factor Models," CREATES Research Papers 2009-09, School of Economics and Management, University of Aarhus.
   
   • Ang, Andrew & Kristensen, Dennis, 2012. "Testing conditional factor models," Journal of Financial Economics, Elsevier, vol. 106(1), pages 132-156.
   • Andrew Ang & Dennis Kristensen, 2011. "Testing Conditional Factor Models," NBER Working Papers 17561, National Bureau of Economic Research, Inc.
2. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
   
   • Dennis Kristensen, 2010. "Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models," CREATES Research Papers 2010-43, School of Economics and Management, University of Aarhus.
   • Dennis Kristensen, 2010. "Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models," Discussion Papers 10-10, University of Copenhagen. Department of Economics.
3. Creel, Michael & Kristensen, Dennis, 2011. "Indirect Likelihood Inference," Dynare Working Papers 8, CEPREMAP.
   
   • Michael Creel & Dennis Kristensen, 2011. "Indirect likelihood inference," UFAE and IAE Working Papers 874.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
   • Michael Creel & Dennis Kristensen, 2011. "Indirect likelihood inference," Working Papers 558, Barcelona Graduate School of Economics.
4. Degui Li & Zudi Lu & Oliver Linton, 2011. "Local Linear Fitting Under Near Epoch Dependence: Uniform consistency with Convergence Rates," Monash Econometrics and Business Statistics Working Papers 16/11, Monash University, Department of Econometrics and Business Statistics.
   
   • Li, Degui & Lu, Zudi & Linton, Oliver, 2012. "Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates," Econometric Theory, Cambridge University Press, vol. 28(05), pages 935-958, October.
5. Michael Vogt & Oliver Linton, 2012. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," CeMMAP working papers CWP23/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
6. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
7. Dennis Kristensen & Bernard Salanié, 2010. "Higher Order Improvements for Approximate Estimators," CAM Working Papers 2010-04, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
   
   • Dennis Kristensen & Bernard Salanie, 2010. "Higher Order Improvements for Approximate Estimators," Discussion Papers 0910-15, Columbia University, Department of Economics.
8. Jiti Gao & Degui Li & Dag Tjøstheim, 2011. "Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series," Monash Econometrics and Business Statistics Working Papers 13/11, Monash University, Department of Econometrics and Business Statistics.
   
   • Jiti Gao & Degui Li & Dag Tjostheim, 2009. "Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series," School of Economics Working Papers 2009-26, University of Adelaide, School of Economics.
9. Debopam Bhattacharya & Shin Kanaya & Margaret Stevens, 2012. "Are University Admissions Academically Fair?," Economics Series Working Papers 608, University of Oxford, Department of Economics.
10. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, School of Economics and Management, University of Aarhus.

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