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Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population
We develop here several goodness-of-fit tests for testing the k-monotonicity
of a discrete density, based on the empirical distribution of the observations.
Our tests are non-parametric, easy to implement and are proved to be
asymptotically of the desired level and consistent. We propose an estimator of
the degree of k-monotonicity of the distribution based on the non-parametric
goodness-of-fit tests. We apply our work to the estimation of the total number
of classes in a population. A large simulation study allows to assess the
performances of our procedures.Comment: 32 pages, 8 figure
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