메뉴 건너뛰기




Volumn 143, Issue 8, 2013, Pages 1249-1272

Energy statistics: A class of statistics based on distances

Author keywords

Distance correlation; Distance covariance; Energy distance; Goodness of fit; Multivariate independence

Indexed keywords


EID: 84878164846     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2013.03.018     Document Type: Review
Times cited : (596)

References (67)
  • 4
    • 78349280725 scopus 로고    scopus 로고
    • Rigid motion invariant two-sample tests
    • Baringhaus L., Franz C. Rigid motion invariant two-sample tests. Statistica Sinica 2010, 20:1333-1361.
    • (2010) Statistica Sinica , vol.20 , pp. 1333-1361
    • Baringhaus, L.1    Franz, C.2
  • 5
    • 58149336555 scopus 로고    scopus 로고
    • Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity
    • Department of Mathematics, University Jaume I, Castellon, Spain, J. Mateu, E. Porcu (Eds.)
    • Berg C. Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity. Positive Definite Functions. From Schoenberg to Space-Time Challenges 2008, Department of Mathematics, University Jaume I, Castellon, Spain. J. Mateu, E. Porcu (Eds.).
    • (2008) Positive Definite Functions. From Schoenberg to Space-Time Challenges
    • Berg, C.1
  • 7
    • 21344498842 scopus 로고
    • Inequalities and positive definite functions arising from a problem in multidimensional scaling
    • Buja A., Logan B.F., Reeds J.A., Shepp L.A. Inequalities and positive definite functions arising from a problem in multidimensional scaling. Annals of Statistics 1994, 22(1):406-438.
    • (1994) Annals of Statistics , vol.22 , Issue.1 , pp. 406-438
    • Buja, A.1    Logan, B.F.2    Reeds, J.A.3    Shepp, L.A.4
  • 8
    • 84945601297 scopus 로고
    • On the composition of elementary errors. II. Statistical applications
    • Cramér H. On the composition of elementary errors. II. Statistical applications. Skandinavisk Aktuarietidskrift 1928, 11:141-180.
    • (1928) Skandinavisk Aktuarietidskrift , vol.11 , pp. 141-180
    • Cramér, H.1
  • 11
    • 21344486242 scopus 로고
    • A consistent test for bivariate dependence
    • Feuerverger A. A consistent test for bivariate dependence. International Statistical Review 1993, 61:419-433.
    • (1993) International Statistical Review , vol.61 , pp. 419-433
    • Feuerverger, A.1
  • 13
    • 84878160771 scopus 로고
    • Generalized Functions, Volume I: Properties and Operations.
    • New York (translation by E. Salatan of the Russian edition of 1958).
    • Gel'fand, I.M., Shilov, G.E., 1964. Generalized Functions, Volume I: Properties and Operations. Academic Press, New York (translation by E. Salatan of the Russian edition of 1958).
    • (1964) Academic Press
    • Gel'fand, I.M.1    Shilov, G.E.2
  • 14
    • 84870308542 scopus 로고    scopus 로고
    • Discussion of. Brownian distance covariance
    • Genovese C. Discussion of. Brownian distance covariance. Annals of Applied Statistics 2009, 3(4):1299-1302. 10.1214/09-AOAS312G.
    • (2009) Annals of Applied Statistics , vol.3 , Issue.4 , pp. 1299-1302
    • Genovese, C.1
  • 17
    • 84859024018 scopus 로고    scopus 로고
    • Strongly consistent nonparametric test of conditional independence
    • Gretton A., Györfi L. Strongly consistent nonparametric test of conditional independence. Statistics and Probability Letters 2012, 82:1145-1150.
    • (2012) Statistics and Probability Letters , vol.82 , pp. 1145-1150
    • Gretton, A.1    Györfi, L.2
  • 18
    • 6744262251 scopus 로고    scopus 로고
    • Goodness-of-fit tests for the Cauchy distribution based on the empirical characteristic function
    • Gurtler N., Henze N. Goodness-of-fit tests for the Cauchy distribution based on the empirical characteristic function. Annals of the Institute of Statistical Mathematics 2000, 52(2):267-286.
    • (2000) Annals of the Institute of Statistical Mathematics , vol.52 , Issue.2 , pp. 267-286
    • Gurtler, N.1    Henze, N.2
  • 19
  • 20
    • 82355174413 scopus 로고    scopus 로고
    • The multiparameter fractional Brownian motion.
    • Springer, Berlin
    • Herbin, E., Merzbach, E., 2007. The multiparameter fractional Brownian motion. In: Math Everywhere. Springer, Berlin, pp. 93-101.
    • (2007) In: Math Everywhere. , pp. 93-101
    • Herbin, E.1    Merzbach, E.2
  • 21
    • 0001744704 scopus 로고
    • A class of statistics with asymptotic normal distribution
    • Hoeffding W. A class of statistics with asymptotic normal distribution. Annals of Mathematic Statistics 1948, 19(3):293-325.
    • (1948) Annals of Mathematic Statistics , vol.19 , Issue.3 , pp. 293-325
    • Hoeffding, W.1
  • 22
    • 67651119911 scopus 로고    scopus 로고
    • Using labeled data to evaluate change detectors in a multivariate streaming environment
    • ISSN 0165-1684
    • Kim A.Y., Marzban C., Percival D.B., Stuetzle W. Using labeled data to evaluate change detectors in a multivariate streaming environment. signal Processing 2009, 89(12):2529-2536. ISSN 0165-1684.
    • (2009) signal Processing , vol.89 , Issue.12 , pp. 2529-2536
    • Kim, A.Y.1    Marzban, C.2    Percival, D.B.3    Stuetzle, W.4
  • 24
    • 84870935881 scopus 로고    scopus 로고
    • Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality
    • Kong J., Klein B.E.K., Klein R., Lee K., Wahba G. Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality. Proceedings of the National Academy of Sciences 2012, 109(50):20352-20357. 10.1073/pnas.1217269109.
    • (2012) Proceedings of the National Academy of Sciences , vol.109 , Issue.50 , pp. 20352-20357
    • Kong, J.1    Klein, B.E.K.2    Klein, R.3    Lee, K.4    Wahba, G.5
  • 25
    • 84878146405 scopus 로고
    • Theory of U-statistics, Mathematics and its Applications
    • Dordrecht (Translated by P.V. Malyshev, D.V. Malyshev from the 1989 Russian original ed.).
    • Koroljuk, V.S., Borovskich, Yu.V., 1994. Theory of U-statistics, Mathematics and its Applications, vol. 273. Kluwer Academic Publishers Group, Dordrecht (Translated by P.V. Malyshev, D.V. Malyshev from the 1989 Russian original ed.).
    • (1994) Kluwer Academic Publishers Group , vol.273
    • Koroljuk, V.S.1    Borovskich Yu, V.2
  • 27
    • 84872351581 scopus 로고    scopus 로고
    • Degenerate U- and V-statistics under ergodicity: asymptotics, bootstrap and applications in statistics
    • Leucht A., Neumann M.H. Degenerate U- and V-statistics under ergodicity: asymptotics, bootstrap and applications in statistics. Annals of the Institute of Statistical Mathematics 2013, 65(2):349-386.
    • (2013) Annals of the Institute of Statistical Mathematics , vol.65 , Issue.2 , pp. 349-386
    • Leucht, A.1    Neumann, M.H.2
  • 28
    • 84870718773 scopus 로고    scopus 로고
    • Feature screening via distance correlation learning
    • Li R., Zhong W., Zhu L. Feature screening via distance correlation learning. Journal of the American Statistical Association 2012, 107(499):1129-1139. 10.1080/01621459.2012.695654.
    • (2012) Journal of the American Statistical Association , vol.107 , Issue.499 , pp. 1129-1139
    • Li, R.1    Zhong, W.2    Zhu, L.3
  • 29
    • 84866493374 scopus 로고    scopus 로고
    • Distance covariance in metric spaces
    • Lyons, R. Distance covariance in metric spaces, Annals of Probability, to appear. 〈〉. http://mypage.iu.edu/~rdlyons/pdf/dcov.pdf.
    • Annals of Probability
    • Lyons, R.1
  • 30
    • 2942611661 scopus 로고
    • Measures of multivariate skewness and kurtosis with applications
    • Mardia K.V. Measures of multivariate skewness and kurtosis with applications. Biometrika 1970, 57:519-530.
    • (1970) Biometrika , vol.57 , pp. 519-530
    • Mardia, K.V.1
  • 31
    • 23744488519 scopus 로고    scopus 로고
    • Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE
    • Matsui M., Takemura A. Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE. Annals of the Institute of Statistical Mathematics 2005, 57(1):183-199.
    • (2005) Annals of the Institute of Statistical Mathematics , vol.57 , Issue.1 , pp. 183-199
    • Matsui, M.1    Takemura, A.2
  • 34
    • 21744459346 scopus 로고    scopus 로고
    • Strict negative definiteness of integrals via complete monotonicity of derivatives
    • Mattner L. Strict negative definiteness of integrals via complete monotonicity of derivatives. Transactions of the American Mathematical Society 1997, 349(8):3321-3342.
    • (1997) Transactions of the American Mathematical Society , vol.349 , Issue.8 , pp. 3321-3342
    • Mattner, L.1
  • 35
    • 84860376365 scopus 로고    scopus 로고
    • Properties of the Székely-Móri symmetry criterion statistics in the case of binary vectors
    • Mensheinin D.O., Zubkov A.M. Properties of the Székely-Móri symmetry criterion statistics in the case of binary vectors. Mathematical Notes 2012, 91(4):62-72.
    • (2012) Mathematical Notes , vol.91 , Issue.4 , pp. 62-72
    • Mensheinin, D.O.1    Zubkov, A.M.2
  • 38
    • 84865559586 scopus 로고    scopus 로고
    • Introducing the discussion paper by Székely and Rizzo
    • Newton M.A. Introducing the discussion paper by Székely and Rizzo. Annals of Applied Statistics 2009, 3(4):1233-1235. 10.1214/09-AOAS34INTRO.
    • (2009) Annals of Applied Statistics , vol.3 , Issue.4 , pp. 1233-1235
    • Newton, M.A.1
  • 40
    • 84907095419 scopus 로고    scopus 로고
    • R: A Language and Environment for Statistical Computing.
    • R Development Core Team, Vienna, Austria. ISBN 3-900051-07-0
    • R Development Core Team, 2012. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, 〈〉. http://www.R-project.org.
    • (2012) R Foundation for Statistical Computing
  • 41
    • 84870360198 scopus 로고    scopus 로고
    • Discussion of. 'Brownian distance covariance'
    • Rémillard B. Discussion of. 'Brownian distance covariance'. Annals of Applied Statistics 2009, 3(4):1295-1298. 10.1214/09-AOAS312F.
    • (2009) Annals of Applied Statistics , vol.3 , Issue.4 , pp. 1295-1298
    • Rémillard, B.1
  • 42
    • 84878152823 scopus 로고    scopus 로고
    • A New Rotation Invariant Goodness-of-Fit Test.
    • Bowling Green State University.
    • Rizzo, M.L., 2002. A New Rotation Invariant Goodness-of-Fit Test. Ph.D. Dissertation. Bowling Green State University.
    • (2002) Ph.D. Dissertation.
    • Rizzo, M.L.1
  • 45
    • 84866238702 scopus 로고    scopus 로고
    • DISCO analysis. a nonparametric extension of analysis of variance
    • Rizzo M.L., Székely G.J. DISCO analysis. a nonparametric extension of analysis of variance. Annals of Applied Statistics 2010, 4(2):1034-1055.
    • (2010) Annals of Applied Statistics , vol.4 , Issue.2 , pp. 1034-1055
    • Rizzo, M.L.1    Székely, G.J.2
  • 47
    • 46549096170 scopus 로고
    • Rapid solution of integral equations of classical potential theory
    • Rokhlin V. Rapid solution of integral equations of classical potential theory. Journal of Computational Physics 1983, 60:187-207.
    • (1983) Journal of Computational Physics , vol.60 , pp. 187-207
    • Rokhlin, V.1
  • 48
    • 84866235173 scopus 로고    scopus 로고
    • Toward an efficient and integrative analysis of limited-choice behavioral experiments
    • Schilling K., Oberdick J., Schilling R.L. Toward an efficient and integrative analysis of limited-choice behavioral experiments. Journal of Neuroscience 2012, 32(37):12651-12656.
    • (2012) Journal of Neuroscience , vol.32 , Issue.37 , pp. 12651-12656
    • Schilling, K.1    Oberdick, J.2    Schilling, R.L.3
  • 49
    • 0001500684 scopus 로고
    • An undulatory theory of the mechanics of atoms and molecules
    • Schrödinger E. An undulatory theory of the mechanics of atoms and molecules. Physical Review 1926, 28(6):1049-1070.
    • (1926) Physical Review , vol.28 , Issue.6 , pp. 1049-1070
    • Schrödinger, E.1
  • 51
    • 67651103353 scopus 로고
    • Potential and Kinetic Energy in Statistics.
    • Lecture Notes. Budapest Institute of Technology (Technical University).
    • Székely, G.J., 1989. Potential and Kinetic Energy in Statistics. Lecture Notes. Budapest Institute of Technology (Technical University).
    • (1989)
    • Székely, G.J.1
  • 53
    • 48349141309 scopus 로고    scopus 로고
    • E-statistics: Energy of Statistical Samples.
    • Department of Mathematics and Statistics Technical Report No. 03-05 (also technical reports by same title, from 2000-2003 and NSA Grant # MDA 904-02-1-0091 (2000-2002).)
    • Székely, G.J., 2003. E-statistics: Energy of Statistical Samples. Bowling Green State University, Department of Mathematics and Statistics Technical Report No. 03-05 (also technical reports by same title, from 2000-2003 and NSA Grant # MDA 904-02-1-0091 (2000-2002).).
    • (2003) Bowling Green State University
    • Székely, G.J.1
  • 55
    • 31244435058 scopus 로고    scopus 로고
    • A characteristic measure of asymmetry and its application for testing diagonal symmetry
    • Székely G.J., Móri T.F. A characteristic measure of asymmetry and its application for testing diagonal symmetry. Communications in Statistics-Theory and Methods 2001, 30(8&9):1633-1639.
    • (2001) Communications in Statistics-Theory and Methods , vol.30 , Issue.8-9 , pp. 1633-1639
    • Székely, G.J.1    Móri, T.F.2
  • 58
    • 33744761434 scopus 로고    scopus 로고
    • Hierarchical clustering via joint between-within distances. extending Ward's minimum variance method
    • Székely G.J., Rizzo M.L. Hierarchical clustering via joint between-within distances. extending Ward's minimum variance method. Journal of Classification 2005, 22(2):151-183.
    • (2005) Journal of Classification , vol.22 , Issue.2 , pp. 151-183
    • Székely, G.J.1    Rizzo, M.L.2
  • 61
    • 84875118601 scopus 로고    scopus 로고
    • The distance correlation t-test of independence in high dimension
    • Székely G.J., Rizzo M.L. The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis 2013, 117:193-213.
    • (2013) Journal of Multivariate Analysis , vol.117 , pp. 193-213
    • Székely, G.J.1    Rizzo, M.L.2
  • 62
    • 50849124115 scopus 로고    scopus 로고
    • Measuring and testing independence by correlation of distances
    • Székely G.J., Rizzo M.L., Bakirov N.K. Measuring and testing independence by correlation of distances. Annals of Statistics 2007, 35(6):2769-2794.
    • (2007) Annals of Statistics , vol.35 , Issue.6 , pp. 2769-2794
    • Székely, G.J.1    Rizzo, M.L.2    Bakirov, N.K.3
  • 63
    • 0000669703 scopus 로고
    • On the asymptotic distributions of differentiable statistical functionals
    • Von Mises R. On the asymptotic distributions of differentiable statistical functionals. Annals of Mathematical Statistics 1947, 2:209-348.
    • (1947) Annals of Mathematical Statistics , vol.2 , pp. 209-348
    • Von Mises, R.1
  • 64
    • 84878116709 scopus 로고    scopus 로고
    • The Energy Goodness-of-Fit Test for Univariate Stable Distributions.
    • Bowling Green State University.
    • Yang, G., 2012. The Energy Goodness-of-Fit Test for Univariate Stable Distributions. Ph.D. Thesis. Bowling Green State University.
    • (2012) Ph.D. Thesis.
    • Yang, G.1
  • 65
    • 33744725160 scopus 로고    scopus 로고
    • Gini's Mean difference. a superior measure of variability for non-normal distributions
    • Yitzhaki S. Gini's Mean difference. a superior measure of variability for non-normal distributions. Metron 2003, 61:285-316.
    • (2003) Metron , vol.61 , pp. 285-316
    • Yitzhaki, S.1
  • 67
    • 84862832581 scopus 로고    scopus 로고
    • Measuring nonlinear dependence in time-series, a distance correlation approach
    • Zhou Z. Measuring nonlinear dependence in time-series, a distance correlation approach. Journal of Time Series Analysis 2012, 33(3):438-457.
    • (2012) Journal of Time Series Analysis , vol.33 , Issue.3 , pp. 438-457
    • Zhou, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.