Nonparametric Kernel Density Estimation Near the Boundary

37 Pages Posted: 19 Oct 2013

See all articles by Peter Malec

Peter Malec

University of Cambridge - Faculty of Economics

Melanie Schienle

Humboldt University of Berlin - School of Business and Economics

Date Written: May 2, 2013

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.

Keywords: Kernel density estimation, boundary correction, asymmetric kernel

JEL Classification: C14

Suggested Citation

Malec, Peter and Schienle, Melanie, Nonparametric Kernel Density Estimation Near the Boundary (May 2, 2013). Available at SSRN: https://ssrn.com/abstract=2342165 or http://dx.doi.org/10.2139/ssrn.2342165

Peter Malec (Contact Author)

University of Cambridge - Faculty of Economics ( email )

Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom

Melanie Schienle

Humboldt University of Berlin - School of Business and Economics ( email )

Spandauer Str. 1
Berlin, D-10099
Germany

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