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Abstract:
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Higher-order histospline estimation uses binned data to generate density estimates which are highly efficient both computationally and in mean integrated squared error convergence. B-splines are weighted in such a way as to restore the correct mass proportions property, in which the probability mass for each histogram bin equals exactly the proportion of the data found in that bin. We will examine the properties of these estimators, and explore extension of these results to settings including density estimation with boundary effects and variable binwidths, multivariate density estimation, and nonparametric regression.
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