Statistical tests based on Renyi entropy estimation
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929712863903744 |
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| author | Cadirci, Mehmet Siddik Evans, Dafydd Leonenko, Nikolai Makogin, Vitali Seleznjev, Oleg |
| author_facet | Cadirci, Mehmet Siddik Evans, Dafydd Leonenko, Nikolai Makogin, Vitali Seleznjev, Oleg |
| contents | Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Renyi entropy based on nearest neighbour distances. We prove the L2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical tests based on Renyi entropy estimation Cadirci, Mehmet Siddik Evans, Dafydd Leonenko, Nikolai Makogin, Vitali Seleznjev, Oleg Methodology Statistics Theory Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Renyi entropy based on nearest neighbour distances. We prove the L2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods. |
| title | Statistical tests based on Renyi entropy estimation |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2502.08654 |