正半轴上密度导数的非参数Gamma核估计
Nonparametric gamma kernel estimators of density derivatives on positive semiaxis
摘要：
本文研究了概率密度函数导数在$[0,\infty)$上有界支撑的非参数估计。在具有非对称伽玛核函数的估计类中查找估计。使用伽马核是因为它们是非负的，根据半轴上的位置改变它们的形状，并且具有其他良好的特性。我们发现的偏差，方差，平均积分平方误差（MISE）的衍生估计的解析表达式。最佳带宽，最佳MISE，和密度导数估计的均方收敛速度也被发现。
英文摘要：
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma kernels is due to the fact they are nonnegative, change their shape depending on the position on the semi-axis and possess other good properties. We found analytical expressions for bias, variance, mean integrated squared error (MISE) of the derivative estimate. An optimal bandwidth, the optimal MISE, and rate of mean square convergence of the estimates for density derivative have also been found.
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