Geodesic
Density estimation via best $L^2$-approximation on classes of step functions
Kybernetika, Tome 53 (2017) no. 2, pp. 198-219

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We establish consistent estimators of jump positions and jump altitudes of a multi-level step function that is the best $L^2$-approximation of a probability density function $f$. If $f$ itself is a step-function the number of jumps may be unknown.
DOI : 10.14736/kyb-2017-2-0198
Classification : 60G44, 62F10, 62G07
Keywords: argmin-theorem; density estimation; step functions; martingale inequalities; multivariate cadlag stochastic processes 
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     title = {Density estimation via best $L^2$-approximation on classes of step functions},
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Ferger, Dietmar; Venz, John. Density estimation via best $L^2$-approximation on classes of step functions. Kybernetika, Tome 53 (2017) no. 2, pp. 198-219. doi: 10.14736/kyb-2017-2-0198

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