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Nonparametric Kernel Density Estimation Near the Boundary

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  • Peter Malec
  • Melanie Schienle

Abstract

Standard fixed symmetric kernel type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. We show that in such settings, alternatives of asymmetric gamma kernel estimators are superior but also differ in asymptotic and finite sample performance conditional on the shape of the density near zero and the exact form of the chosen kernel. We therefore suggest a refined version of the gamma kernel with an additional tuning parameter according to the shape of the density close to the boundary. We also provide a data-driven method for the appropriate choice of the modified gamma kernel estimator. In an extensive simulation study we compare the performance of this refined estimator to standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. We find that the finite sample performance of the proposed new estimator is superior in all settings. Two empirical applications based on high-frequency stock trading volumes and realized volatility forecasts demonstrate the usefulness of the proposed methodology in practice.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2012-047.

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Length: 32 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2012-047

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Keywords: Kernel density estimation; boundary correction; asymmetric kernel;

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