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Volumn 15, Issue 5, 2013, Pages 1609-1623

A novel nonparametric distance estimator for densities with error bounds

Author keywords

Generalized differential divergences; Generalized differential entropies; Hellinger metric; Heterocedastic data; Nonparametric estimators; Tsallis entropy

Indexed keywords


EID: 84878353547     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e15051609     Document Type: Article
Times cited : (5)

References (41)
  • 1
    • 84941476533 scopus 로고
    • Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen.
    • Hellinger, E. Neue Begrandung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Crelle 1909, 210-271.
    • (1909) Crelle , pp. 210-271
    • Hellinger, E.1
  • 2
    • 0001199215 scopus 로고
    • A general class of coefficients of divergence of one distribution from another.
    • Ali S.M. Silvey S.D.,A general class of coefficients of divergence of one distribution from another. ,J. R. Stat. Soc. Series B. ;1966,28,131-142
    • (1966) J. R. Stat. Soc. Series B. , vol.28 , pp. 131-142
    • Ali, S.M.1    Silvey, S.D.2
  • 3
    • 0029690146 scopus 로고    scopus 로고
    • Entropy, divergence and distance measures with econometric applications.
    • Ullah, A. Entropy, divergence and distance measures with econometric applications. J. Stat. Plan Inferace 1996, 49, 137-162.
    • (1996) J. Stat. Plan Inferace , vol.49 , pp. 137-162
    • Ullah, A.1
  • 4
    • 33845299971 scopus 로고    scopus 로고
    • Information Theoretic Learning Renyi's Entropy and Kernel Perspectives;
    • Springer: New York, NY, USA,
    • Principe, J.C.Information Theoretic Learning Renyi's Entropy and Kernel Perspectives; Springer: New York, NY, USA, 2010.
    • (2010)
    • Principe, J.C.1
  • 5
    • 85057428046 scopus 로고    scopus 로고
    • Statistical Inference Based on Divergence Measures;
    • Chapman and Hall/CRC: Boca Raton, FL, USA,
    • Pardo, L. Statistical Inference Based on Divergence Measures; Chapman and Hall/CRC: Boca Raton, FL, USA, 2005; p. 483.
    • (2005) , pp. 483
    • Pardo, L.1
  • 7
    • 49949144765 scopus 로고
    • The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming.
    • Bregman, L.M. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 1967, 7, 200-217.
    • (1967) USSR Comput. Math. Math. Phys. , vol.7 , pp. 200-217
    • Bregman, L.M.1
  • 8
    • 29444455987 scopus 로고
    • Fisher and inverse probability.
    • Jeffreys, H. Fisher and inverse probability. Int. Stat. Rev. 1974, 42, 1-3.
    • (1974) Int. Stat. Rev. , vol.42 , pp. 1-3
    • Jeffreys, H.1
  • 9
    • 0022115467 scopus 로고
    • Cross entropy, dissimilarity measures, and characterizations of quadratic entropy.
    • Rao, C.R.; Nayak, T.K. Cross entropy, dissimilarity measures, and characterizations of quadratic entropy. IEEE Trans. Inf. Theory 1985, 31, 589-593.
    • (1985) IEEE Trans. Inf. Theory , vol.31 , pp. 589-593
    • Rao, C.R.1    Nayak, T.K.2
  • 10
    • 0025952277 scopus 로고
    • Divergence measures based on the Shannon Entropy.
    • Lin, J.H. Divergence measures based on the Shannon Entropy. IEEE Trans. Inf. Theory 1991,37, 145-151.
    • (1991) IEEE Trans. Inf. Theory , vol.37 , pp. 145-151
    • Lin, J.H.1
  • 12
    • 51449107790 scopus 로고    scopus 로고
    • Compressed signal reconstruction using the correntropy induced metric.
    • In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing,Las Vegas, NV, USA, March 31-April 4,
    • Seth, S.; Principe, J.C. Compressed signal reconstruction using the correntropy induced metric.In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing,Las Vegas, NV, USA, March 31-April 4, 2008; pp. 3845-3848.
    • (2008)
    • Seth, S.1    Principe, J.C.2
  • 13
    • 0034224418 scopus 로고    scopus 로고
    • Some inequalities for information divergence and Related measures of discrimination.
    • Topsoe, F. Some inequalities for information divergence and Related measures of discrimination.IEEE Trans. Inf. Theory 2000, 46, 1602-1609.
    • (2000) IEEE Trans. Inf. Theory , vol.46
    • Topsoe, F.1
  • 14
    • 33947426775 scopus 로고    scopus 로고
    • On divergences and informations in statistics and information theory.
    • Liese, F.; Vajda, I. On divergences and informations in statistics and information theory. IEEE Trans. Inf. Theory 2006, 52, 4394-4412.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 4394-4412
    • Liese, F.1    Vajda, I.2
  • 15
    • 0036839620 scopus 로고    scopus 로고
    • Hypothesis testing: A model selection approach.
    • Cubedo, M.; Oller, J.M. Hypothesis testing: A model selection approach. J. Stat. Plan. Inference2002, 108, 3-21.
    • (2002) J. Stat. Plan. Inference , vol.108 , pp. 3-21
    • Cubedo, M.1    Oller, J.M.2
  • 16
    • 85043087771 scopus 로고    scopus 로고
    • Non-parametric Hellingers Metric.
    • In Proceedings of CMNE/CILANCE 2007, Porto,Portugal, 13-15 June 2007.t
    • Puga, A.T.; Non-parametric Hellingers Metric. In Proceedings of CMNE/CILANCE 2007, Porto,Portugal, 13-15 June 2007.
    • (2007)
    • Puga A.T.1    2
  • 17
    • 84980082105 scopus 로고
    • Transmission of information. Bell Syst.
    • Hartley, R.V.L. Transmission of information. Bell Syst. Tech. J. 1928, 7, 535-563.
    • (1928) Tech. J. , vol.7 , pp. 535-563
    • Hartley, R.V.L.1
  • 18
    • 84856043672 scopus 로고
    • A mathematical theory of communication.
    • Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27, 379-423.
    • (1948) Bell Syst. Tech. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 19
    • 0002408684 scopus 로고
    • On Measures of Entropy and Information, Fourth Berkeley Symposium on Math.Statist.
    • and Prob; University of California: Berkeley: CA, USA,
    • Rényi, A. On Measures of Entropy and Information, Fourth Berkeley Symposium on Math.Statist. and Prob; University of California: Berkeley: CA, USA, 1961; Volume 1, pp. 547-561.
    • (1961) , vol.1 , pp. 547-561
    • Rényi, A.1
  • 20
    • 0004305358 scopus 로고    scopus 로고
    • Nonextensive Entropy: Interdisciplinary Applications
    • Oxford University Press: New York, NY, USA
    • Nonextensive Entropy: Interdisciplinary Applications; Gell-Mann, M.; Tsallis, C., Eds.; Oxford University Press: New York, NY, USA, 2004.
    • (2004)
    • Gell-Mann, M.1    Tsallis, C.2
  • 21
    • 0032273847 scopus 로고    scopus 로고
    • Two-state paramagnetism induced by Tsallis and Renyi statistics.
    • Wolf, C. Two-state paramagnetism induced by Tsallis and Renyi statistics. Int. J. .Theor. Phys.1998, 37, 2433-2438.
    • (1998) Int. J. .Theor. Phys. , vol.37 , pp. 2433-2438
    • Wolf, C.1
  • 23
    • 0001924657 scopus 로고
    • Thermodynamic stability conditions for the Tsallis and Renyi entropies.
    • Ramshaw, J.D. Thermodynamic stability conditions for the Tsallis and Renyi entropies. Phys.Lett. A 1995, 198, 119-121.
    • (1995) Phys.Lett. A , vol.198 , pp. 119-121
    • Ramshaw, J.D.1
  • 24
    • 0036896227 scopus 로고    scopus 로고
    • On choosing and bounding probability metrics.
    • Gibbs, A.L.; Su, F.E. On choosing and bounding probability metrics. Int. Stat. Rev. 2002, 70,419-435.
    • (2002) Int. Stat. Rev. , vol.70 , pp. 419-435
    • Gibbs, A.L.1    Su, F.E.2
  • 25
  • 26
    • 0003545910 scopus 로고
    • Multivariate Density Estimation: Theory, Practice, and Visualization;
    • Wiley:New York, NY, USA, 1992. Entropy 2013, 15 1623
    • Scott, D.W. Multivariate Density Estimation: Theory, Practice, and Visualization; Wiley:New York, NY, USA, 1992.
    • (1992)
    • Scott, D.W.1
  • 27
    • 0003391450 scopus 로고
    • Non-Uniform Random Variate Generation;
    • Springer-Verlag: New York, NY, USA,
    • Devroye, L. Non-Uniform Random Variate Generation; Springer-Verlag: New York, NY, USA, 1986.
    • (1986)
    • Devroye, L.1
  • 28
    • 51249180311 scopus 로고
    • The student distribution and the principle of maximum-entropy.
    • Preda, V.C. The student distribution and the principle of maximum-entropy. Ann. Inst. Stat. Math.1982, 34, 335-338.
    • (1982) Ann. Inst. Stat. Math. , vol.34 , pp. 335-338
    • Preda, V.C.1
  • 29
    • 85043082616 scopus 로고
    • Maximum-Entropy Models in Science and Engineering;
    • Kapur, J.N. Maximum-Entropy Models in Science and Engineering; Wiley: New York, NY, USA, 1989.
    • (1989) Wiley: New York, NY, USA,
    • Kapur, J.N.1
  • 30
    • 85043067156 scopus 로고    scopus 로고
    • The Probable Error of a Mean. Available online: (accessed on 28 April 2013)
    • The Probable Error of a Mean. Available online: http://www.jstor.org/discover/10.2307/2331554?uid=2&uid=4&sid=21102107492741/ (accessed on 28 April 2013).
    • (2013)
  • 31
    • 54349103517 scopus 로고    scopus 로고
    • A class of Renyi information estimators for multidimensional densities.
    • Leonenko, N.; Pronzato, L.; Savani, V. A class of Renyi information estimators for multidimensional densities. Ann. Stat. 2008, 36, 2153-2182.
    • (2008) Ann. Stat. , vol.36 , pp. 2153-2182
    • Leonenko, N.1    Pronzato, L.2    Savani, V.3
  • 32
    • 79953752369 scopus 로고    scopus 로고
    • k-nearest neighbor based consistent entropy estimation for hyperspherical distributions
    • Li, S.; Mnatsakanov, R.M.; Andrew, M.E. k-nearest neighbor based consistent entropy estimation for hyperspherical distributions. Entropy 2011, 13, 650-667.
    • (2011) Entropy , vol.13 , pp. 650-667
    • Li, S.1    Mnatsakanov, R.M.2    Andrew, M.E.3
  • 33
    • 84885830378 scopus 로고    scopus 로고
    • Laws of large numbers and nearest neighbor distances. In Advances in Directional and Linear Statistics
    • Wells, M.T., SenGupta, A., Eds.; Physica-Verlag: Heidelberg, Germany, 2011;
    • Penrose, M.D.; Yukich, J.E. Laws of large numbers and nearest neighbor distances. In Advances in Directional and Linear Statistics; Wells, M.T., SenGupta, A., Eds.; Physica-Verlag: Heidelberg, Germany, 2011; pp. 189-199.
    • (2011) , pp. 189-199
    • Penrose, M.D.1    Yukich, J.E.2
  • 34
    • 77953501154 scopus 로고    scopus 로고
    • Nearest neighbor estimates of entropy for multivariate circular distributions.
    • Misra, N.; Singh, H.; Hnizdo, V. Nearest neighbor estimates of entropy for multivariate circular distributions. Entropy 2010, 12, 1125-1144.
    • (2010) Entropy , vol.12 , pp. 1125-1144
    • Misra, N.1    Singh, H.2    Hnizdo, V.3
  • 36
    • 65749108082 scopus 로고    scopus 로고
    • Divergence estimation for multidimensional densities via k-nearest-neighbor distances.
    • Wang, Q.; Kulkarni, S.R.; Verdu, S. Divergence estimation for multidimensional densities via k-nearest-neighbor distances. IEEE Trans. Inf. Theory 2009, 55, 2392-2405.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , pp. 2392-2405
    • Wang, Q.1    Kulkarni, S.R.2    Verdu, S.3
  • 37
    • 54349107695 scopus 로고    scopus 로고
    • Choice of neighbor order in nearest-neighbor classification.
    • Hall, P.; Park, B.U.; Samworth, R.J. Choice of neighbor order in nearest-neighbor classification.Ann. Stat. 2008, 36, 2135-2152.
    • (2008) Ann. Stat. , vol.36 , pp. 2135-2152
    • Hall, P.1    Park, B.U.2    Samworth, R.J.3
  • 38
    • 33845748728 scopus 로고    scopus 로고
    • Melting point prediction employing k-nearest neighbor algorithms and genetic parameter optimization.
    • Nigsch, F.; Bender, A.; van Buuren, B.; Tissen, J.; Nigsch, E.; Mitchell, J.B.O. Melting point prediction employing k-nearest neighbor algorithms and genetic parameter optimization. J. Chem. Inf. Model. 2006, 46, 2412-2422.
    • (2006) J. Chem. Inf. Model. , vol.46 , pp. 2412-2422
    • Nigsch, F.1    Bender, A.2    van Buuren, B.3    Tissen, J.4    Nigsch, E.5    Mitchell, J.B.O.6
  • 39
    • 84947205653 scopus 로고    scopus 로고
    • When Is Nearest Neighbor Meaningful? In Proceedings of 7the International Conference on Database Theory,
    • Jerusalem, Israel,10-12 January 1999;
    • Beyer, K.; Goldstein, J.; Ramakrishnan, R.; Shaft, U. When Is Nearest Neighbor Meaningful? In Proceedings of 7the International Conference on Database Theory, Jerusalem, Israel,10-12 January 1999; pp. 217-235.
    • (1999) , pp. 217-235
    • Beyer, K.1    Goldstein, J.2    Ramakrishnan, R.3    Shaft, U.4
  • 40
    • 79551605534 scopus 로고    scopus 로고
    • Total bregman divergence and its applications to DTI analysis.
    • Vemuri, B.C.; Liu, M.; Amari, S.I.; Nielsen, F. Total bregman divergence and its applications to DTI analysis. IEEE Trans. Med. Imag. 2011, 30, 475-483.
    • (2011) IEEE Trans. Med. Imag. , vol.30 , pp. 475-483
    • Vemuri, B.C.1    Liu, M.2    Amari, S.I.3    Nielsen, F.4
  • 41
    • 84867817160 scopus 로고    scopus 로고
    • Shape retrieval using hierarchical total bregman soft clustering.
    • Liu, M.; Vemuri, B.; Amari, S. I.; Nielsen, F. Shape retrieval using hierarchical total bregman soft clustering. IEEE T. Pattern Anal. 2012, 34, 2407-2419.
    • (2012) IEEE T. Pattern Anal. , vol.34 , pp. 2407-2419
    • Liu, M.1    Vemuri, B.2    Amari, S.I.3    Nielsen, F.4


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