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A Note on the Asymptotic Normality of the Kernel Deconvolution Density Estimator with Logarithmic Chi-Square Noise

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  • Yang Zu

    (Department of Economics, City University London, Northampton Square, EC1V 0HB London, UK)

Abstract

This paper studies the asymptotic normality for the kernel deconvolution estimator when the noise distribution is logarithmic chi-square; both identical and independently distributed observations and strong mixing observations are considered. The dependent case of the result is applied to obtain the pointwise asymptotic distribution of the deconvolution volatility density estimator in discrete-time stochastic volatility models.

Suggested Citation

  • Yang Zu, 2015. "A Note on the Asymptotic Normality of the Kernel Deconvolution Density Estimator with Logarithmic Chi-Square Noise," Econometrics, MDPI, vol. 3(3), pages 1-16, July.
    • Handle: RePEc:gam:jecnmx:v:3:y:2015:i:3:p:561-576:d:52948
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    References listed on IDEAS

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    1. F. Comte & V. Genon‐Catalot, 2006. "Penalized Projection Estimator for Volatility Density," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 875-893, December.
    2. Masry, E., 1993. "Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 47-68, January.
    3. Delaigle, A. & Gijbels, I., 2004. "Practical bandwidth selection in deconvolution kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 249-267, March.
    4. Viktor Todorov & George Tauchen, 2012. "Inverse Realized Laplace Transforms for Nonparametric Volatility Density Estimation in Jump-Diffusions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 622-635, June.
    5. Bert Van Es & Hae‐Won Uh, 2005. "Asymptotic Normality of Kernel‐Type Deconvolution Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 467-483, September.
    6. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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