Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population
| Autor: | Jade Giguelay, Sylvie Huet |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
education.field_of_study Applied Mathematics 010102 general mathematics Population Nonparametric statistics Estimator 01 natural sciences Empirical distribution function Unimodality Convexity 010104 statistics & probability Computational Mathematics Computational Theory and Mathematics Goodness of fit Applied mathematics Probability distribution 0101 mathematics education Mathematics |
| Zdroj: | Computational Statistics & Data Analysis. 127:96-115 |
| ISSN: | 0167-9473 |
| DOI: | 10.1016/j.csda.2018.02.006 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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