Title: Tree-Structured Histogram Estimation Based on a Simple Class of Wavelets
Abstract: Adaptive multivariate histograms that are obtained through recursive partitioning of the sample space are studied. The central idea is to consider the tree-structured histogram as a wavelet estimator based on the orthogonal system of Haar functions. From the formula for the mean squared error a spatially adaptive data-driven smoothing method is proposed leading to an unequal bin width histogram.
Keywords: Multivariate histogram, adaptive histogram, tree-structured methods, wavelets, Haar functions
Creation-Date: August 1993
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