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Central Limit Theorem for Asymmetric Kernel Functionals

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  • Fernandes, M.

Abstract

Asymmetric kernels are quite useful for the estimation of density functions which have bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. This paper extends the central limit theorem for degenerate U-statistics in order to compute the limiting distribution of certain asymmetric kernel functionals.

Suggested Citation

  • Fernandes, M., 2000. "Central Limit Theorem for Asymmetric Kernel Functionals," Economics Working Papers eco2000/1, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2000/1
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    References listed on IDEAS

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    1. Bruce M. Brown, 1999. "Beta-Bernstein Smoothing for Regression Curves with Compact Support," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 47-59.
    2. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    3. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    4. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    5. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
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    Cited by:

    1. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    2. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    3. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes," CIRJE F-Series CIRJE-F-573, CIRJE, Faculty of Economics, University of Tokyo.
    4. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    5. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    6. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    7. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-27, June.
    8. Marcelo Fernandes & Eduardo Mendes & Olivier Scaillet, 2015. "Testing for symmetry and conditional symmetry using asymmetric kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 649-671, August.
    9. Muhammad Hanif, 2011. "Reweighted Nadaraya-Watson estimator of scalar diffusion models by using asymmetric kernels," Far East Journal of Psychology and Business, Far East Research Centre, vol. 4(5), pages 53-69, July.
    10. Flôres Junior, Renato Galvão, 2004. "On the use (fulness) of CGE modelling in trade negotiations and policy," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 564, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).

    More about this item

    Keywords

    STATISTICS ; MATHEMATICS;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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