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Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population

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  • Giguelay, J.
  • Huet, S.

Abstract

The development of nonparametric procedures for testing shape constraint (monotonicity, convexity, unimodality, etc.) has received increasing interest. Nevertheless, testing the k-monotonicity of a discrete density for k larger than 2 has received little attention. To deal with this issue, several testing procedures based on the empirical distribution of the observations have been developed. They are non-parametric, easy to implement and proven to be asymptotically of the desired level and consistent. An estimator of the degree of k-monotonicity of the distribution is presented. An application to the estimation of the total number of classes in a population is proposed. A large simulation study makes it possible to assess the performances of the various procedures.

Suggested Citation

  • Giguelay, J. & Huet, S., 2018. "Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 96-115.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:96-115
    DOI: 10.1016/j.csda.2018.02.006
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    References listed on IDEAS

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    1. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

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