메뉴 건너뛰기




Volumn 58, Issue 7, 2012, Pages 4135-4159

Estimation of nonlinear functionals of densities with confidence

Author keywords

Adaptive estimators; bias and variance tradeoff; bipartite k nearest neighbor ( NN) graphs; concentration bounds; convergence rates; data splitting estimators; entropy estimation

Indexed keywords

ADAPTIVE ESTIMATORS; BIAS AND VARIANCE; CONCENTRATION BOUNDS; CONVERGENCE RATES; DATA-SPLITTING ESTIMATORS; ENTROPY ESTIMATION; K-NEAREST NEIGHBORS;

EID: 84862560441     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2012.2195549     Document Type: Article
Times cited : (57)

References (39)
  • 1
    • 85032752338 scopus 로고    scopus 로고
    • Applications of entropic spanning graphs
    • Sep.
    • A. O. Hero, B. Ma, O. Michel, and J. Gorman, "Applications of entropic spanning graphs," IEEE Signal Process. Mag., vol. 19, no. 5, pp. 85-95, Sep. 2002.
    • (2002) IEEE Signal Process. Mag. , vol.19 , Issue.5 , pp. 85-95
    • Hero, A.O.1    Ma, B.2    Michel, O.3    Gorman, J.4
  • 2
    • 21944455302 scopus 로고    scopus 로고
    • Image registration in high dimensional feature space
    • presented at the presented at the, San Jose, CA, Jan.
    • H. Neemuchwala and A. O. Hero, "Image registration in high dimensional feature space," presented at the presented at the SPIE Conf. Electron. Imag., San Jose, CA, Jan. 2005.
    • (2005) SPIE Conf. Electron. Imag.
    • Neemuchwala, H.1    Hero, A.O.2
  • 4
    • 33847290520 scopus 로고    scopus 로고
    • Mining anomalies using traffic feature distributions
    • A. Lakhina, M. Crovella, and C. Diot, "Mining anomalies using traffic feature distributions," in Proc. ACM SIGCOMM, 2005, pp. 217-228.
    • (2005) Proc. ACM SIGCOMM , pp. 217-228
    • Lakhina, A.1    Crovella, M.2    Diot, C.3
  • 5
    • 0019543368 scopus 로고
    • Image data compression: A review
    • Mar.
    • A. Jain, "Image data compression: A review," Proc. IEEE, vol. 69, no. 3, pp. 349-389, Mar. 1981.
    • (1981) Proc. IEEE , vol.69 , Issue.3 , pp. 349-389
    • Jain, A.1
  • 6
    • 0002260546 scopus 로고
    • A test for normality based on sample entropy
    • O. Vasicek, "A test for normality based on sample entropy," J. R. Statist. Soc. Series B (Methodol.), vol. 38, pp. 54-59, 1976.
    • (1976) J. R. Statist. Soc. Series B (Methodol. , vol.38 , pp. 54-59
    • Vasicek, O.1
  • 8
    • 0001044948 scopus 로고
    • Estimating parameters in continuous univariate distributions with a shifted origin
    • R. C. H. Cheng and N. A. K. Amin, "Estimating parameters in continuous univariate distributions with a shifted origin," J. R. Statist. Soc. Series B (Methodol.), vol. 11, pp. 394-403, 1983.
    • (1983) J. R. Statist. Soc. Series B (Methodol. , vol.11 , pp. 394-403
    • Cheng, R.C.H.1    Amin, N.A.K.2
  • 9
    • 0002646747 scopus 로고
    • The maximum spacing method. An estimation method related to the maximum likelihood method
    • B. Ranneby, "The maximum spacing method. An estimation method related to the maximum likelihood method," Scand. J. Statist., vol. 11, pp. 93-112, 1984.
    • (1984) Scand. J. Statist. , vol.11 , pp. 93-112
    • Ranneby, B.1
  • 10
    • 54349103517 scopus 로고    scopus 로고
    • A class of Rényi information estimators for multidimensional densities
    • N. Leonenko, L. Prozanto, and V. Savani, "A class of Rényi information estimators for multidimensional densities," Ann. Statist., vol. 36, pp. 2153-2182, 2008.
    • (2008) Ann. Statist. , vol.36 , pp. 2153-2182
    • Leonenko, N.1    Prozanto, L.2    Savani, V.3
  • 12
    • 84860647823 scopus 로고    scopus 로고
    • Estimation of Rényi entropy and mutual information based on generalized nearest-neighbor graphs
    • Mar.
    • D. Pál, B. Póczos, and C. Szepesvári, "Estimation of Rényi entropy and mutual information based on generalized nearest-neighbor graphs," ArXiv E-Prints, Mar. 2010.
    • (2010) ArXiv E-Prints
    • Pál, D.1    Póczos, B.2    Szepesvári, C.3
  • 13
    • 0002545991 scopus 로고
    • Estimating functionals related to a density by class of statistics based on spacing
    • B. van Es, "Estimating functionals related to a density by class of statistics based on spacing," Scand. J. Statist., 1992.
    • (1992) Scand. J. Statist.
    • Van Es, B.1
  • 14
    • 80054814166 scopus 로고    scopus 로고
    • A new class of randomvector entropy estimators and its applications in testing statistical hypotheses
    • M. Goria, N. Leonenko, V. Mergel, and P. L. N. Inverardi, "A new class of randomvector entropy estimators and its applications in testing statistical hypotheses," Nonparametric Statist., 2004.
    • (2004) Nonparametric Statist.
    • Goria, M.1    Leonenko, N.2    Mergel, V.3    Inverardi, P.L.N.4
  • 16
    • 26444495559 scopus 로고    scopus 로고
    • Divergence estimation of continuous distributions based on data-dependent partitions
    • Sep.
    • Q.Wang, S. R. Kulkarni, and S. Verdú, "Divergence estimation of continuous distributions based on data-dependent partitions," IEEE Trans. Inf. Theory, vol. 51, no. 9, pp. 3064-3074, Sep. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.9 , pp. 3064-3074
    • Wang, Q.1    Kulkarni, S.R.2    Verdú, S.3
  • 17
    • 84939024947 scopus 로고
    • A nonparametric estimation of the entropy for absolutely continuous distributions (corresp.)
    • May
    • I. Ahmad and P.-E. Lin, "A nonparametric estimation of the entropy for absolutely continuous distributions (corresp.)," IEEE Trans. Inf. Theory, vol. IT-22, no. 3, pp. 372-375, May 1976.
    • (1976) IEEE Trans. Inf. Theory , vol.IT-22 , Issue.3 , pp. 372-375
    • Ahmad, I.1    Lin, P.-E.2
  • 18
    • 0032690752 scopus 로고    scopus 로고
    • Best asymptotic normality of the kernel density entropy estimator for smooth densities
    • May
    • P. B. Eggermont and V. N. LaRiccia, "Best asymptotic normality of the kernel density entropy estimator for smooth densities," IEEE Trans. Inf. Theory, vol. 45, no. 4, pp. 1321-1326, May 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.4 , pp. 1321-1326
    • Eggermont, P.B.1    LaRiccia, V.N.2
  • 19
    • 0001667487 scopus 로고
    • Estimating integrated squared density derivatives: Sharp best order of convergence estimates
    • Oct.
    • P. J. Bickel and Y. Ritov, "Estimating integrated squared density derivatives: Sharp best order of convergence estimates," Sankhya: Indian J. Statist., vol. 50, pp. 381-393, Oct. 1988.
    • (1988) Sankhya: Indian J. Statist. , vol.50 , pp. 381-393
    • Bickel, P.J.1    Ritov, Y.2
  • 20
    • 38249035197 scopus 로고
    • Estimation of integrated squared density derivatives
    • P. Hall and J. S. Marron, "Estimation of integrated squared density derivatives," Statist. Prob. Lett., vol. 6, pp. 109-115, 1987.
    • (1987) Statist. Prob. Lett. , vol.6 , pp. 109-115
    • Hall, P.1    Marron, J.S.2
  • 21
    • 21844523744 scopus 로고
    • Estimation of integral functions of a density
    • L. Birge and P. Massart, "Estimation of integral functions of a density," Ann. Statist., vol. 23, no. 1, pp. 11-29, 1995.
    • (1995) Ann. Statist. , vol.23 , Issue.1 , pp. 11-29
    • Birge, L.1    Massart, P.2
  • 22
    • 55849092871 scopus 로고    scopus 로고
    • Uniform in bandwidth estimation of integral functionals of the density function
    • E. Giné and D. Mason, "Uniform in bandwidth estimation of integral functionals of the density function," Scand. J. Statist., vol. 35, pp. 739-761, 2008.
    • (2008) Scand. J. Statist. , vol.35 , pp. 739-761
    • Giné, E.1    Mason, D.2
  • 23
    • 22944483445 scopus 로고    scopus 로고
    • Edgeworth approximation ofmultivariate differential entropy
    • M.M. V. Hulle, "Edgeworth approximation ofmultivariate differential entropy," Neural Comput., vol. 17, no. 9, pp. 1903-1910, 2005.
    • (2005) Neural Comput. , vol.17 , Issue.9 , pp. 1903-1910
    • Hulle, M.M.V.1
  • 24
    • 77958588617 scopus 로고    scopus 로고
    • Estimating divergence functionals and the likelihood ratio by convex risk minimization
    • Nov.
    • X. Nguyen, M. J. Wainwright, and M. I. Jordan, "Estimating divergence functionals and the likelihood ratio by convex risk minimization," IEEE Trans. Inf. Theory, vol. 56, no. 11, pp. 5847-5861, Nov. 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.11 , pp. 5847-5861
    • Nguyen, X.1    Wainwright, M.J.2    Jordan, M.I.3
  • 25
    • 0030490121 scopus 로고    scopus 로고
    • Efficient estimation of integral functionals of a density
    • B. Laurent, "Efficient estimation of integral functionals of a density," Ann. Statist., vol. 24, no. 2, pp. 659-681, 1996.
    • (1996) Ann. Statist. , vol.24 , Issue.2 , pp. 659-681
    • Laurent, B.1
  • 27
    • 0011274512 scopus 로고    scopus 로고
    • Asymptotic moments of nearest neighbor distance distributions
    • D. Evans, A. Jones, and W. M. Schmidt, "Asymptotic moments of nearest neighbor distance distributions," in Proc. R. Soc. A, 2008, vol. 458, pp. 2839-2849.
    • (2008) Proc. R. Soc. A , vol.458 , pp. 2839-2849
    • Evans, D.1    Jones, A.2    Schmidt, W.M.3
  • 28
    • 64149109685 scopus 로고    scopus 로고
    • Gaussian limits for generalized spacings
    • Y. Baryshnikov, M. D. Penrose, and J. Yukich, "Gaussian limits for generalized spacings," Ann. Appl. Prob., vol. 19, no. 1, pp. 158-185, 2009.
    • (2009) Ann. Appl. Prob. , vol.19 , Issue.1 , pp. 158-185
    • Baryshnikov, Y.1    Penrose, M.D.2    Yukich, J.3
  • 29
    • 54849429557 scopus 로고    scopus 로고
    • A law of large numbers for nearest neighbor statistics
    • D. Evans, "A law of large numbers for nearest neighbor statistics," in Proc. R. Soc. A, 2008, vol. 464, pp. 3175-3192.
    • (2008) Proc. R. Soc. A , vol.464 , pp. 3175-3192
    • Evans, D.1
  • 32
    • 0001791128 scopus 로고
    • Multivariate-nearest neighbor density estimates
    • Y. P. Mack and M. Rosenblatt, "Multivariate-nearest neighbor density estimates," J. Multivariate Anal., vol. 9, no. 1, pp. 1-15, 1979.
    • (1979) J. Multivariate Anal. , vol.9 , Issue.1 , pp. 1-15
    • Mack, Y.P.1    Rosenblatt, M.2
  • 33
    • 27644572056 scopus 로고
    • Optimization of-nearest-neighbor density estimates
    • May
    • K. Fukunaga and L. D. Hostetler, "Optimization of-nearest-neighbor density estimates," IEEE Trans. Inf. Theory, vol. IT-19, no. 3, pp. 320-326, May 1973.
    • (1973) IEEE Trans. Inf. Theory , vol.IT-19 , Issue.3 , pp. 320-326
    • Fukunaga, K.1    Hostetler, L.D.2
  • 35
    • 0000165508 scopus 로고
    • Consistency properties of nearest neighbor density function estimators
    • D. S. Moore and J. W. Yackel, "Consistency properties of nearest neighbor density function estimators," Ann. Statist., 1977.
    • (1977) Ann. Statist.
    • Moore, D.S.1    Yackel, J.W.2
  • 37
    • 78650093364 scopus 로고    scopus 로고
    • Correction:Aclass of Rényi information estimators for multidimensional densities
    • N. Leonenko, L. Prozanto, and V. Savani, "Correction:Aclass of Rényi information estimators for multidimensional densities," Ann. Statist., vol. 38, pp. 3837-3838, 2010.
    • Ann. Statist. , vol.38 , Issue.2010 , pp. 3837-3838
    • Leonenko, N.1    Prozanto, L.2    Savani, V.3
  • 38
    • 80052232668 scopus 로고    scopus 로고
    • Weighted k-nn graphs for Rényi entropy estimation in high dimensions
    • K. Sricharan and A. Hero, "Weighted k-nn graphs for Rényi entropy estimation in high dimensions," in Proc. IEEE Statist. Signal Process. Workshop, 2011, pp. 773-776.
    • (2011) Proc. IEEE Statist. Signal Process. Workshop , pp. 773-776
    • Sricharan, K.1    Hero, A.2
  • 39
    • 33745476564 scopus 로고    scopus 로고
    • Fast optimal bandwidth selection for kernel density estimation," Proc. 6th
    • V. C. Raykar and R. Duraiswami, "Fast optimal bandwidth selection for kernel density estimation," Proc. 6th SIAM Int. Conf. Data Mining, pp. 524-528, 2006.
    • (2006) SIAM Int. Conf. Data Mining , pp. 524-528
    • Raykar, V.C.1    Duraiswami, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.