摘要翻译：
我们用局部多项式逼近未知密度$F$的对数来估计密度及其导数。保证了该估计量是非负的，并且在$F$支持的内部和边界上达到相同的最优收敛速度。因此，该估计器非常适合于需要非负密度估计的应用，如在半参数极大似然估计中。此外，我们还证明了我们的估计器在渐近性能和计算简单性方面都优于其他基于核的方法。仿真结果表明，当使用Epanechnikov核和最优带宽序列时，我们的方法在有限样本中的性能与这些方法相似，这些方法可以用于最优输入，即Epanechnikov核和最优带宽序列。进一步的仿真证据表明，如果研究者改变输入并选择更大的带宽，我们的方法甚至可以渐近地改善这些优化方案。我们提供几种语言的代码。
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英文标题：
《Estimates of derivatives of (log) densities and related objects》
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作者：
Joris Pinkse, Karl Schurter
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最新提交年份：
2020
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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.
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PDF链接：
https://arxiv.org/pdf/2006.01328