关于光滑密度的严格概率密度估计
On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm
摘要：
本文证明了McKay（1993 a和b）根据Abramson（1982）的早期发现提出的可变带宽密度估计器在有界集上以极大极小速率逼近$C^4(\mathbb R^d)$中的密度函数，其中它们所基于的初始密度估计是远离零的有界的。Jones McKay和Hu（1994）提出了一个更复杂的估计量来近似$C^6(\mathbb R)$中的密度，也证明了在相同类型的集合上以超范数获得极大极小率。这些估计量是严格的概率密度。
英文摘要：
It is shown that the variable bandwidth density estimator proposed by McKay (1993a and b) following earlier findings by Abramson (1982) approximates density functions in $C^4(\mathbb R^d)$ at the minimax rate in the supremum norm over bounded sets where the preliminary density estimates on which they are based are bounded away from zero. A somewhat more complicated estimator proposed by Jones McKay and Hu (1994) to approximate densities in $C^6(\mathbb R)$ is also shown to attain minimax rates in sup norm over the same kind of sets. These estimators are strict probability densities.
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