Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2017
- DOI:
- 10.48550/arXiv.1708.08676
- arXiv:
- arXiv:1708.08676
- Bibcode:
- 2017arXiv170808676G
- Keywords:
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- Statistics - Methodology
- E-Print:
- 32 pages, 8 figures