메뉴 건너뛰기




Volumn 13, Issue 1, 2011, Pages 1-27

The Generalized Cross Entropy Method, with Applications to Probability Density Estimation

Author keywords

Bandwidth selection; Calculus of variations; Cross entropy; Functional optimization; Information theory; Kernel smoothing; Monte Carlo simulation; Statistical modeling

Indexed keywords


EID: 78651424177     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-009-9133-7     Document Type: Article
Times cited : (54)

References (65)
  • 1
    • 0001110699 scopus 로고
    • On bandwidth variation in kernel estimates-a square root law
    • Abramson IS (1982) On bandwidth variation in kernel estimates-a square root law. Ann Stat 10: 1217-1223.
    • (1982) Ann Stat , vol.10 , pp. 1217-1223
    • Abramson, I.S.1
  • 2
    • 0346202017 scopus 로고    scopus 로고
    • Modelling the distribution of stamp paper thickness via finite normal mixtures: the 1872 stamp issue of Mexico revisited
    • Basford KE, McLachlan GJ, York MG (1997) Modelling the distribution of stamp paper thickness via finite normal mixtures: the 1872 stamp issue of Mexico revisited. J Appl Stat 24: 169-179.
    • (1997) J Appl Stat , vol.24 , pp. 169-179
    • Basford, K.E.1    McLachlan, G.J.2    York, M.G.3
  • 3
    • 0023349263 scopus 로고
    • Penalty functions and duality in stochastic programming via φ{symbol} divergence functionals
    • Ben-Tal A, Teboulle M (1987) Penalty functions and duality in stochastic programming via φ{symbol} divergence functionals. Math Oper Res 12: 224-240.
    • (1987) Math Oper Res , vol.12 , pp. 224-240
    • Ben-Tal, A.1    Teboulle, M.2
  • 5
    • 0026116433 scopus 로고
    • Duality relationships for entropy-like minimization problems
    • Borwein JM, Lewis AS (1991) Duality relationships for entropy-like minimization problems. SIAM J Control Optim 29: 325-338.
    • (1991) SIAM J Control Optim , vol.29 , pp. 325-338
    • Borwein, J.M.1    Lewis, A.S.2
  • 7
    • 39149135658 scopus 로고    scopus 로고
    • ePrintsUQ, BSc (Hons) thesis,Department of Mathematics, School of Physical Sciences, The University of Queensland
    • Botev ZI (2005) Stochastic methods for optimization and machine learning. ePrintsUQ, BSc (Hons) thesis, Department of Mathematics, School of Physical Sciences, The University of Queensland. http://eprint. uq. edu. au/archive/00003377/.
    • (2005) Stochastic methods for optimization and machine learning
    • Botev, Z.I.1
  • 8
    • 46949101175 scopus 로고    scopus 로고
    • Non-asymptotic bandwidth selection for density estimation of discrete data
    • Botev ZI, Kroese DP (2008) Non-asymptotic bandwidth selection for density estimation of discrete data. Methodol Comput Appl Probab 10: 435-451.
    • (2008) Methodol Comput Appl Probab , vol.10 , pp. 435-451
    • Botev, Z.I.1    Kroese, D.P.2
  • 9
    • 0001688136 scopus 로고
    • A comparative study of some kernel-based nonparametric density estimators
    • Bowman AW (1985) A comparative study of some kernel-based nonparametric density estimators. J Stat Comput Simul 21: 313-327.
    • (1985) J Stat Comput Simul , vol.21 , pp. 313-327
    • Bowman, A.W.1
  • 10
    • 0003448243 scopus 로고
    • Cross-validation in nonparametric estimation of probabilities and probability densities
    • Bowman AW, Hall P, Titterington DM (1984) Cross-validation in nonparametric estimation of probabilities and probability densities. Biometrika 71: 341-351.
    • (1984) Biometrika , vol.71 , pp. 341-351
    • Bowman, A.W.1    Hall, P.2    Titterington, D.M.3
  • 12
    • 0030351528 scopus 로고    scopus 로고
    • An entropy criterion for assessing the number of clusters in a mixture model
    • Celeux G, Soromenho G (1996) An entropy criterion for assessing the number of clusters in a mixture model. J Classif 13: 195-212.
    • (1996) J Classif , vol.13 , pp. 195-212
    • Celeux, G.1    Soromenho, G.2
  • 13
    • 0041974049 scopus 로고
    • Marginal likelihood from the gibbs output
    • Chib S (1982) Marginal likelihood from the gibbs output. J Am Stat Assoc 90: 1313-1321.
    • (1982) J Am Stat Assoc , vol.90 , pp. 1313-1321
    • Chib, S.1
  • 14
    • 0000787802 scopus 로고
    • Bandwidth selection for kernel density estimation
    • Chiu ST (1991) Bandwidth selection for kernel density estimation. Ann Stat 19: 1883-1905.
    • (1991) Ann Stat , vol.19 , pp. 1883-1905
    • Chiu, S.T.1
  • 15
    • 0001569844 scopus 로고
    • A class of measures of informativity of observation channels
    • Csiszár I (1972) A class of measures of informativity of observation channels. Period Math Hung 2: 191-213.
    • (1972) Period Math Hung , vol.2 , pp. 191-213
    • Csiszár, I.1
  • 16
    • 0000493799 scopus 로고
    • Dual methods in entropy maximization. Applications to some problems in crystalography
    • Decarreau A, Hilhorst D, Lemarechal C, Navaza J (1992) Dual methods in entropy maximization. Applications to some problems in crystalography. SIAM J Optim 2: 173-197.
    • (1992) SIAM J Optim , vol.2 , pp. 173-197
    • Decarreau, A.1    Hilhorst, D.2    Lemarechal, C.3    Navaza, J.4
  • 17
    • 0003863896 scopus 로고
    • Wiley series in probability and mathematical statistics, New York: Wiley
    • 1 view. Wiley series in probability and mathematical statistics. Wiley, New York.
    • (1985) 1 View
    • Devroye, L.1    Gyofri, L.2
  • 19
    • 0142039770 scopus 로고    scopus 로고
    • Probability density estimation from optimally condensed data samples
    • Girolami M, He C (2003) Probability density estimation from optimally condensed data samples. IEEE Trans Pattern Anal Mach Intell 25(10): 1253-1264.
    • (2003) IEEE Trans Pattern Anal Mach Intell , vol.25 , Issue.10 , pp. 1253-1264
    • Girolami, M.1    He, C.2
  • 20
    • 4544297796 scopus 로고    scopus 로고
    • 2 optimal non-parametric density estimator
    • 2 optimal non-parametric density estimator. Pattern Recogn Lett 25: 1389-1397.
    • (2004) Pattern Recogn Lett , vol.25 , pp. 1389-1397
    • Girolami, M.1    He, C.2
  • 21
    • 0000418028 scopus 로고
    • On Kullback-Leibler loss and density estimation
    • Hall P (1987) On Kullback-Leibler loss and density estimation. Ann Stat 15: 1491-1519.
    • (1987) Ann Stat , vol.15 , pp. 1491-1519
    • Hall, P.1
  • 22
    • 0033611817 scopus 로고    scopus 로고
    • Reducing bias in curve estimation by use of weights
    • Hall P, Turlach BA (1999) Reducing bias in curve estimation by use of weights. Comput Stat Data Anal 30: 67-86.
    • (1999) Comput Stat Data Anal , vol.30 , pp. 67-86
    • Hall, P.1    Turlach, B.A.2
  • 23
    • 0002453010 scopus 로고
    • Quantification methods of classification processes: concepts of structural α entropy
    • Havrda JH, Charvat F (1967) Quantification methods of classification processes: concepts of structural α entropy. Kybernatica 3: 30-35.
    • (1967) Kybernatica , vol.3 , pp. 30-35
    • Havrda, J.H.1    Charvat, F.2
  • 24
    • 0006380024 scopus 로고
    • Philatelic mixtures and multimodal densities
    • Izenman AJ, Sommer CJ (1988) Philatelic mixtures and multimodal densities. J Am Stat Assoc 83: 941-953.
    • (1988) J Am Stat Assoc , vol.83 , pp. 941-953
    • Izenman, A.J.1    Sommer, C.J.2
  • 25
    • 11944266539 scopus 로고
    • Information theory and statistical mechanics
    • Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106: 621-630.
    • (1957) Phys Rev , vol.106 , pp. 621-630
    • Jaynes, E.T.1
  • 26
    • 0030517778 scopus 로고    scopus 로고
    • Progress in data-based bandwidth selection for kernel density estimation
    • Jones MC, Marron JS, Sheather SJ (1996) Progress in data-based bandwidth selection for kernel density estimation. Comput Stat 11: 337-381.
    • (1996) Comput Stat , vol.11 , pp. 337-381
    • Jones, M.C.1    Marron, J.S.2    Sheather, S.J.3
  • 32
    • 0001927585 scopus 로고
    • On information and sufficiency
    • Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22: 79-86.
    • (1951) Ann Math Stat , vol.22 , pp. 79-86
    • Kullback, S.1    Leibler, R.A.2
  • 34
    • 84972487778 scopus 로고
    • Model specification: the views of fisher and neyman, and later developments
    • Lehmann EL (1990) Model specification: the views of fisher and neyman, and later developments. Stat Sci 5: 160-168.
    • (1990) Stat Sci , vol.5 , pp. 160-168
    • Lehmann, E.L.1
  • 35
    • 0033438066 scopus 로고    scopus 로고
    • Bandwidth selection: classical or plug-in
    • Loader CR (1999a) Bandwidth selection: classical or plug-in. Ann Stat 27: 415-438.
    • (1999) Ann Stat , vol.27 , pp. 415-438
    • Loader, C.R.1
  • 37
    • 0002584853 scopus 로고
    • An asymptotically efficient solution to the bandwidth problem of kernel density estimation
    • Marron JS (1985) An asymptotically efficient solution to the bandwidth problem of kernel density estimation. Ann Stat 13: 1011-1023.
    • (1985) Ann Stat , vol.13 , pp. 1011-1023
    • Marron, J.S.1
  • 38
    • 0001366850 scopus 로고
    • Exact mean integrated squared error
    • Marron JS, Wand MP (1992) Exact mean integrated squared error. Ann Stat 20: 712-736.
    • (1992) Ann Stat , vol.20 , pp. 712-736
    • Marron, J.S.1    Wand, M.P.2
  • 39
    • 0006397963 scopus 로고
    • A simple root n bandwidth selector
    • Marron JS, Jones MC, Park BU (1991) A simple root n bandwidth selector. Ann Stat 19(4): 1919-1932.
    • (1991) Ann Stat , vol.19 , Issue.4 , pp. 1919-1932
    • Marron, J.S.1    Jones, M.C.2    Park, B.U.3
  • 41
    • 78651442015 scopus 로고    scopus 로고
    • Contribution to the discussion of paper by S. Richardson and P. J. Green
    • Mclachlan GJ, Peel D (1997) Contribution to the discussion of paper by S. Richardson and P. J. Green. J R Stat Soc Ser B Stat Methodol 59: 779-780.
    • (1997) J R Stat Soc Ser B Stat Methodol , vol.59 , pp. 779-780
    • Mclachlan, G.J.1    Peel, D.2
  • 43
    • 3843114488 scopus 로고    scopus 로고
    • Advanced search algorithms for information-theoretic learning with kernel-based estimators
    • Morejon RA, Principe JC (2004) Advanced search algorithms for information-theoretic learning with kernel-based estimators. IEEE Trans Neural Netw 15: 874-884.
    • (2004) IEEE Trans Neural Netw , vol.15 , pp. 874-884
    • Morejon, R.A.1    Principe, J.C.2
  • 44
    • 78651439127 scopus 로고    scopus 로고
    • Multivariate density estimation: a support vector machine approach
    • Mukherjee S, Vapnik V (1999) Multivariate density estimation: a support vector machine approach. Massachusetts Institute of Technology. ftp://publications. ai. mit. edu/ai-publications/1500-1999/AIM-1653. ps.
    • (1999) Massachusetts Institute of Technology
    • Mukherjee, S.1    Vapnik, V.2
  • 46
    • 0036647905 scopus 로고    scopus 로고
    • An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems
    • Principe JC, Erdogmus D (2002) An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems. IEEE Trans Signal Process 50: 1780-1786.
    • (2002) IEEE Trans Signal Process , vol.50 , pp. 1780-1786
    • Principe, J.C.1    Erdogmus, D.2
  • 47
    • 18244378520 scopus 로고    scopus 로고
    • On bayesian analysis of mixtures with an unknown number of components (with discussion)
    • Richardson S, Green PJ (1997) On bayesian analysis of mixtures with an unknown number of components (with discussion). J R Stat Soc Ser B Stat Methodol 59: 731-792.
    • (1997) J R Stat Soc Ser B Stat Methodol , vol.59 , pp. 731-792
    • Richardson, S.1    Green, P.J.2
  • 48
    • 0000795635 scopus 로고
    • Density estimation with confidence sets exemplified by super-clusters and voids in the galaxies
    • Roeder K (1990) Density estimation with confidence sets exemplified by super-clusters and voids in the galaxies. J Am Stat Assoc 85: 617-624.
    • (1990) J Am Stat Assoc , vol.85 , pp. 617-624
    • Roeder, K.1
  • 49
    • 16244401100 scopus 로고    scopus 로고
    • The stochastic minimum cross-entropy method for combinatorial optimization and rare-event estimation
    • Rubinstein RY (2005) The stochastic minimum cross-entropy method for combinatorial optimization and rare-event estimation. Methodol Comput Appl Probab 7: 5-50.
    • (2005) Methodol Comput Appl Probab , vol.7 , pp. 5-50
    • Rubinstein, R.Y.1
  • 52
    • 21344491756 scopus 로고
    • Bias reduction in kernel density estimation by smoothed empirical transformations
    • Ruppert D, Cline DBH (1994) Bias reduction in kernel density estimation by smoothed empirical transformations. Ann Stat 22: 185-210.
    • (1994) Ann Stat , vol.22 , pp. 185-210
    • Ruppert, D.1    Cline, D.B.H.2
  • 53
  • 54
    • 0035419755 scopus 로고    scopus 로고
    • Parametric statistical modeling by minimum integrated square error
    • Scott DW (2001) Parametric statistical modeling by minimum integrated square error. Technimetrics 43: 274-285.
    • (2001) Technimetrics , vol.43 , pp. 274-285
    • Scott, D.W.1
  • 55
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27: 379-423, 623-659.
    • (1948) Bell Syst Tech J , vol.27
    • Shannon, C.E.1
  • 58
    • 0001048793 scopus 로고
    • An asymptotically optimal window selection rule for kernel density estimates
    • Stone CJ (1984) An asymptotically optimal window selection rule for kernel density estimates. Ann Stat 12: 1285-1297.
    • (1984) Ann Stat , vol.12 , pp. 1285-1297
    • Stone, C.J.1
  • 59
    • 21144472623 scopus 로고
    • Variable kernel density estimation
    • Terrell GR, Scott DW (1992) Variable kernel density estimation. Ann Stat 20: 1236-1265.
    • (1992) Ann Stat , vol.20 , pp. 1236-1265
    • Terrell, G.R.1    Scott, D.W.2
  • 61
    • 33646516485 scopus 로고
    • Possible generalization of Boltzmann-Gibbs statistics
    • Tsallis C (1988) Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52: 479.
    • (1988) J Stat Phys , vol.52 , pp. 479
    • Tsallis, C.1
  • 65
    • 0030335917 scopus 로고    scopus 로고
    • Nonparametric importance sampling
    • Zhang P (1996) Nonparametric importance sampling. J Am Stat Assoc 91(435): 1245-1253.
    • (1996) J Am Stat Assoc , vol.91 , Issue.435 , pp. 1245-1253
    • Zhang, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.