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

2017/08/29 by Jade Giguelay, Giguelay, Jade, Sylvie Huet +1 · 1 citation
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #Survey Sampling and Estimation Techniques

paper · pdf · doi:10.48550/arxiv.1708.08676

openalex publication_date 2017/08/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We develop here several goodness-of-fit tests for testing the k-monotonicity\nof a discrete density, based on the empirical distribution of the observations.\nOur tests are non-parametric, easy to implement and are proved to be\nasymptotically of the desired level and consistent. We propose an estimator of\nthe degree of k-monotonicity of the distribution based on the non-parametric\ngoodness-of-fit tests. We apply our work to the estimation of the total number\nof classes in a population. A large simulation study allows to assess the\nperformances of our procedures.\n

Cited by

• Parametric convergence rate of some nonparametric estimators in mixtures of power series distributions

Related

• Asymptotic theory for nonparametric testing of k-monotonicity in discrete distributions
• Big Data on the Rise: Testing monotonicity of distributions
• Bayesian Inference for k-Monotone Densities with Applications to Multiple Testing
• New Lower Bounds for Testing Monotonicity and Log Concavity of Distributions
• Nonparametric Bayesian testing for monotonicity