（对数）密度的导数的估计和相关对象
Estimates of derivatives of (log) densities and related objects
摘要：
我们估计的密度和它的衍生物使用一个局部多项式近似的对数未知的密度$f$。该估计器保证是非负的，并达到相同的最佳收敛速度的内部以及$f$的支持的边界。因此，该估计非常适合于需要非负密度估计的应用，例如半参数最大似然估计。此外，我们表明，我们的估计与其他基于核的方法相比，无论是在渐近性能和计算方便。仿真结果证实，我们的方法可以在有限样本中执行类似的这些替代方法时，他们使用的最佳输入，即Epanechnikov内核和最佳选择的带宽序列。进一步的模拟证据表明，如果研究人员修改输入并选择更大的带宽，我们的方法甚至可以渐进地改进这些优化的替代方案。我们提供多种语言的代码。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
