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Chapter 1 Constrained density estimation

A methodology is proposed for non-parametric density estimation, constrained by the known expected values of one or more functions. In particular, prescribing the first moment –the mean of the distribution– is a requirement for the density estimation associated to martingales. The problem is addressed through the introduction of a family of maps that transform the unknown density into an isotropic Gaussian, while adjusting the prescribed moments of the estimated density. 1.