ESTIMATES OF DERIVATIVES OF (LOG) DENSITIES AND RELATED OBJECTS
提出一种通过对数密度函数的局部多项式逼近来估计密度及其导数的方法，保证非负性且在支撑集内部和边界达到相同最优收敛速度，适用于需要非负密度估计的半参数最大似然估计等应用。
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density function f . The estimator is guaranteed to be non-negative and achieves the same optimal rate of convergence in the interior as on the boundary of the support of f . The estimator is therefore well-suited to applications in which non-negative 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 or better in finite samples compared to these alternative methods when they are used with optimal inputs, that is, an Epanechnikov kernel and optimally chosen bandwidth sequence. We provide code in several languages.