Beta kernel estimators for density functions
Computational Statistics & Data Analysis
Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval
Computational Statistics & Data Analysis
Nonparametric density estimation for positive time series
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Generalized Birnbaum-Saunders kernel density estimators and an analysis of financial data
Computational Statistics & Data Analysis
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Standard fixed symmetric kernel-type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. It is shown that, in such settings, alternatives of asymmetric gamma kernel estimators are superior, but also differ in asymptotic and finite sample performance conditionally on the shape of the density near zero and the exact form of the chosen kernel. Therefore, a refined version of the gamma kernel with an additional tuning parameter adjusted according to the shape of the density close to the boundary is suggested. A data-driven method for the appropriate choice of the modified gamma kernel estimator is also provided. An extensive simulation study compares the performance of this refined estimator to those of standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. It is found 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.