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A class of Rényi information estimators for multidimensional densities
Open accessAbstract
A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in ℝm is presented. These estimators are based on the kth nearest-neighbor distances computed from a sample of N i.i.d. vectors with distribution f. We show that entropies of any order q, including Shannon’s entropy, can be estimated consistently with minimal assumptions on f. Moreover, we show that it is straightforward to extend the nearest-neighbor method to estimate the statistical distance between two distributions using one i.i.d. sample from each.
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Cites
Possible generalization of Boltzmann-Gibbs statistics
Tsallis, C. (1988) · Journal of Statistical Physics · doi:10.1007/bf01016429 · Cited by 9,589
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HLAVACKOVASCHINDLER, K., PALUS, M., VEJMELKA, M., & BHATTACHARYA, J. (2007) · Physics Reports · doi:10.1016/j.physrep.2006.12.004 · Cited by 800
Kullback-Leibler divergence estimation of continuous distributions
Perez-Cruz, F. (2008) · 2008 IEEE International Symposium on Information Theory · doi:10.1109/isit.2008.4595271 · Cited by 400
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Metadata
- Authors
- Leonenko, N., Pronzato, L., & Savani, V.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2008-10-01
- Volume
- 36
- Issue
- 5
- Pages
- 2153-2182
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1981050900
- Cited by
- 240
- References
- 1
- FWCI
- 14.14
- Type
- journal article
- Language
- en
- Open access
- green
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