We present a new method for reconstructing the density function underlying a given histogram. First we analyze the univariate case taking the approximating function in a class of "quadratic-like" splines with variable degrees. For the analogous bivariate problem we introduce a new scheme based on the "Boolean sum" of univariate B-splines and show that for a proper choice of the degrees, the splines are positive and satisfy local monotonicity constraints.
Costantini, P., Pelosi, F. (2007). Shape-preserving Histogram Approximation. ADVANCES IN COMPUTATIONAL MATHEMATICS, 26, 205-230 [10.1007/s10444-004-8008-2].
Shape-preserving Histogram Approximation
PELOSI, FRANCESCA
2007-01-01
Abstract
We present a new method for reconstructing the density function underlying a given histogram. First we analyze the univariate case taking the approximating function in a class of "quadratic-like" splines with variable degrees. For the analogous bivariate problem we introduce a new scheme based on the "Boolean sum" of univariate B-splines and show that for a proper choice of the degrees, the splines are positive and satisfy local monotonicity constraints.File in questo prodotto:
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