论文标题
（log）密度和相关对象的衍生物的估计值
Estimates of derivatives of (log) densities and related objects
论文作者
论文摘要
我们使用局部多项式近似估计密度及其衍生物与未知密度$ f $的对数。保证估算器是非负数的，并且在内部和支撑$ F $的边界中达到了相同的最佳收敛速率。因此，估计器非常适合需要非负密度估计值的应用，例如在半摩匹仪最大似然估计中。此外，我们表明我们的估计器与其他基于内核的方法相比，无论是在渐近性能和计算方便方面。仿真结果证实，当我们的方法与最佳输入（即Epanechnikov内核和最佳选择的带宽序列）一起使用时，我们的方法可以在有限样本中与这些替代方法相似。进一步的仿真证据表明，如果研究人员修改输入并选择较大的带宽，我们的方法甚至可以徒劳地改善这些优化的替代方案。我们提供几种语言的代码。
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior as well as the boundary of the support of $f$. The estimator is therefore well-suited to applications in which nonnegative density estimates are required, such as in semiparametric maximum likelihood estimation. In addition, we show that our estimator compares favorably with other kernel-based methods, both in terms of asymptotic performance and computational ease. Simulation results confirm that our method can perform similarly in finite samples to these alternative methods when they are used with optimal inputs, i.e. an Epanechnikov kernel and optimally chosen bandwidth sequence. Further simulation evidence demonstrates that, if the researcher modifies the inputs and chooses a larger bandwidth, our approach can even improve upon these optimized alternatives, asymptotically. We provide code in several languages.
