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The discrete convex least-squares estimator of a probability mass function

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Motivated by the estimation of the species abundance distribution in ecology, we are interested in estimating a discrete convex probability mass function. The discrete convex least-squares estimator is considered. Although it does not have a closed form, the estimator can be computed thanks to a support reduction algorithm. The weak limiting distribution of the estimator is derived: it can be defined via a certain convex projection of a Gaussian vector.

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