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Estimating the Derivative of a Convex Density

We obtain a relation between the time between two bird‐catchings and the total resting period of a bird, leading to the problem of estimating the derivative of a convex density. We state a fundamental result on the nonparametric maximum likelihood estimator of a convex density. Further, we derive the optimal rate in the minimax risk sense for estimating the derivative of a convex density.