Nonparametric Kernel Density Estimation Near the Boundary
Nonparametric Kernel Density Estimation Near the Boundary
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DOI：
10.2139/ssrn.2342165
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
P. Malec;M. Schienle
中科院分区：
文献类型：
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作者：
P. Malec;M. Schienle
已知标准的固定对称核型密度估计会遇到正随机变量的大概率质量接近于零的问题。结果表明，在这样的设置中，非对称伽玛核估计的替代品是上级，但也不同的渐近和有限样本性能条件的形状的密度接近零和所选的内核的确切形式。因此，一个改进的版本的伽玛内核与一个额外的调整参数调整根据接近边界的密度的形状建议。还提供了用于适当选择修改的伽马核估计器的数据驱动的方法。一个广泛的模拟研究比较了这种改进的估计的性能，标准的伽玛核估计和标准的边界校正和调整的固定内核。结果发现，所提出的新估计的有限样本性能是优越的上级在所有设置。基于高频股票交易量和已实现波动率预测的两个实证应用证明了所提出的方法在实践中的实用性。
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.