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Consistency of data-driven histogram methods for density estimation and classification
The Annals of Statistics
We present general sufficient conditions for the almost sure L 1 -consistency of histogram density estimates based on data-dependent partitions. Analogous conditions guarantee the almost-sure risk consistency of histogram classification schemes based on data-dependent partitions. Multivariate data is considered throughout. In each case, the desired consistency requires shrinking cells, subexponential growth of a combinatorial complexity measure, and sub-linear growth of the number of cells. Itdoi:10.1214/aos/1032894460 fatcat:dfcqcdzcczh53pvgobgsb5p7hq