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Density estimation via best $L^{2}$ -approximation on classes of step functions

Dietmar Ferger; John Venz — 2017

Kybernetika

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.

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Density estimation via best L 2 -approximation on classes of step functions

Density estimation via best $L^{2}$ -approximation on classes of step functions