Bin width selection in multivariate histograms by the combinatorial method
Bin width selection in multivariate histograms by the combinatorial method
复制标题
通过组合方法选择多元直方图中的箱宽度
作者：
L. Devroye;G. Lugosi
**摘要**
我们给出了几种多元直方图密度估计量，它们在一个常数因子和一个附加项$$O\left( {\sqrt {\log {n \mathord{\left/ {\vphantom {n n}} \right. \kern-\nulldelimiterspace} n}} } \right)$$的范围内是普遍的$L_1$最优的。箱宽是通过作者在《密度估计中的组合方法》（施普林格出版社，2001年）中所开发的组合方法来选择的。本文解决了那本书中遗留的一个问题。
AbstractWe present several multivariate histogram density estimates that are universallyL1-optimal to within a constant factor and an additive term
$$O\left( {\sqrt {\log {n \mathord{\left/ {\vphantom {n n}} \right. \kern-\nulldelimiterspace} n}} } \right)$$
. The bin widths are chosen by the combinatorial method developed by the authors inCombinatorial Methods in Density Estimation (Springer-Verlag, 2001). The present paper solves a problem left open in that book.