Bin width selection in multivariate histograms by the combinatorial method

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.

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