正半轴上密度导数伽玛核估计的数据驱动带宽选择
Data-driven bandwidth choice for gamma kernel estimates of density derivatives on the positive semi-axis
摘要：
在某些应用中，有必要估计定义在正半轴上的概率密度的导数。概率密度及其导数的非参数估计的质量受到平滑参数（带宽）的强烈影响。本文给出了密度导数伽玛核估计的最优光滑参数的表达式。对于这一参数，基于称为“经验法则”和“交叉验证”的方法构建了数据驱动的估计。质量的估计验证和证明的麦克斯韦和韦布尔分布产生的密度导数的例子。
英文摘要：
In some applications it is necessary to estimate derivatives of probability densities defined on the positive semi-axis. The quality of nonparametric estimates of the probability densities and their derivatives are strongly influenced by smoothing parameters (bandwidths). In this paper an expression for the optimal smoothing parameter of the gamma kernel estimate of the density derivative is obtained. For this parameter data-driven estimates based on methods called "rule of thumb" and "cross-validation" are constructed. The quality of the estimates is verified and demonstrated on examples of density derivatives generated by Maxwell and Weibull distributions.
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