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Volumn 18, Issue 2, 2009, Pages 481-504

A functional EM algorithm for mixing density estimation via nonparametric penalized likelihood maximization

Author keywords

Mixture model; Nonparametric maximum penalized likelihood estimate; Ordinary differential equation with boundary conditions

Indexed keywords


EID: 77950649478     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2009.07111     Document Type: Article
Times cited : (19)

References (42)
  • 1
    • 0003796630 scopus 로고
    • New York: Academic Press
    • Adams, R. (1975), Sobolev Spaces, New York: Academic Press.
    • (1975) Sobolev Spaces
    • Adams, R.1
  • 3
    • 84966237528 scopus 로고
    • A regularity theory for variational problems with higher order derivatives
    • Clarke, F. H., and Vinter, R. B. (1990), "A Regularity Theory for Variational Problems With Higher Order Derivatives," Transactions of the American Mathematical Society, 320, 227-251.
    • (1990) Transactions of the American Mathematical Society , vol.320 , pp. 227-251
    • Clarke, F.H.1    Vinter, R.B.2
  • 4
    • 0000684078 scopus 로고
    • Nonparametric maximum likelihood estimation of probability densities by penalty function methods
    • De Montricher, G. M., Tapia, R. A., and Thompson, J. R. (1975), "Nonparametric Maximum Likelihood Estimation of Probability Densities by Penalty Function Methods," The Annals of Statistics, 3, 1329-1348.
    • (1975) The Annals of Statistics , vol.3 , pp. 1329-1348
    • De Montricher, G.M.1    Tapia, R.A.2    Thompson, J.R.3
  • 7
    • 21844524494 scopus 로고
    • Maximum smoothed likelihood density estimation for inverse problems
    • Eggermont, P. P. B., and LaRiccia, V. N. (1995), "Maximum Smoothed Likelihood Density Estimation for Inverse Problems," The Annals of Statistics, 23, 199-220.
    • (1995) The Annals of Statistics , vol.23 , pp. 199-220
    • Eggermont, P.P.B.1    LaRiccia, V.N.2
  • 8
    • 0031318605 scopus 로고    scopus 로고
    • Nonlinearly smoothed EM density estimation with automated smoothing parameter selection for nonparametric deconvolution problems
    • Eggermont, P., and LaRiccia, V. (1997), "Nonlinearly Smoothed EM Density Estimation With Automated Smoothing Parameter Selection for Nonparametric Deconvolution Problems," Journal of the American Statistical Association, 92, 1451-1458.
    • (1997) Journal of the American Statistical Association , vol.92 , pp. 1451-1458
    • Eggermont, P.1    LaRiccia, V.2
  • 9
    • 0000867838 scopus 로고
    • On the optimal rates of convergence for nonparametric deconvolution problems
    • Fan, J. (1991), "On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems," The Annals of Statistics, 19, 1257-1272.
    • (1991) The Annals of Statistics , vol.19 , pp. 1257-1272
    • Fan, J.1
  • 11
    • 0000451036 scopus 로고
    • Nonparametric roughness penalties for probability densities
    • Good, I. J., and Gaskins, R. A. (1971), "Nonparametric Roughness Penalties for Probability Densities," Biometrika, 58, 255-277.
    • (1971) Biometrika , vol.58 , pp. 255-277
    • Good, I.J.1    Gaskins, R.A.2
  • 12
    • 0031326719 scopus 로고    scopus 로고
    • Nonparametric estimation of a mixing density via the kernel method
    • Goutis, C. (1997), "Nonparametric Estimation of a Mixing Density via the Kernel Method," Journal of the American Statistical Association, 92, 1445-1450.
    • (1997) Journal of the American Statistical Association , vol.92 , pp. 1445-1450
    • Goutis, C.1
  • 13
    • 0000357775 scopus 로고
    • On the use of the EM algorithm for penalized likelihood estimation
    • Ser. B
    • Green, P. J. (1990), "On the Use of the EM Algorithm for Penalized Likelihood Estimation," Journal of the Royal Statistical Society, Ser. B, 52, 443-452.
    • (1990) Journal of the Royal Statistical Society , vol.52 , pp. 443-452
    • Green, P.J.1
  • 15
    • 21144484353 scopus 로고
    • Smoothing spline density estimation: A dimensionless automatic algorithm
    • Gu, C. (1993), "Smoothing Spline Density Estimation: A Dimensionless Automatic Algorithm," Journal of the American Statistical Association, 88, 495-504.
    • (1993) Journal of the American Statistical Association , vol.88 , pp. 495-504
    • Gu, C.1
  • 16
    • 21144466328 scopus 로고
    • Smoothing spline density estimation: Theory
    • Gu, C., and Qiu, C. (1993), "Smoothing Spline Density Estimation: Theory," The Annals of Statistics, 21, 217-234.
    • (1993) The Annals of Statistics , vol.21 , pp. 217-234
    • Gu, C.1    Qiu, C.2
  • 19
    • 0000319983 scopus 로고
    • Speed of estimation in positron emission tomography and related inverse problems
    • Johnstone, I. M., and Silverman, B. W. (1990), "Speed of Estimation in Positron Emission Tomography and Related Inverse Problems," The Annals of Statistics, 18, 251-280.
    • (1990) The Annals of Statistics , vol.18 , pp. 251-280
    • Johnstone, I.M.1    Silverman, B.W.2
  • 20
    • 0000187262 scopus 로고
    • An orthogonal series density estimation approach to reconstructing positron emission tomography images
    • Jones, M. C., and Silverman, B. W. (1989), "An Orthogonal Series Density Estimation Approach to Reconstructing Positron Emission Tomography Images," Journal of Applied Statistics, 16, 177-191.
    • (1989) Journal of Applied Statistics , vol.16 , pp. 177-191
    • Jones, M.C.1    Silverman, B.W.2
  • 22
    • 0009371766 scopus 로고
    • Consistency of a nonparametric penalized likelihood estimator of the probability desity function
    • Klonias, V. K. (1982), "Consistency of a Nonparametric Penalized Likelihood Estimator of the Probability Desity Function," The Annals of Statistics, 10, 811-824.
    • (1982) The Annals of Statistics , vol.10 , pp. 811-824
    • Klonias, V.K.1
  • 23
    • 0032373643 scopus 로고    scopus 로고
    • Log-density estimation in linear inverse problems
    • Koo, J.-Y., and Chung, H.-Y. (1998), "Log-Density Estimation in Linear Inverse Problems," The Annals of Statistics, 26, 335-362.
    • (1998) The Annals of Statistics , vol.26 , pp. 335-362
    • Koo, J.-Y.1    Chung, H.-Y.2
  • 25
    • 84936016001 scopus 로고
    • Nonparametric maximum likelihood estimation of a mixing distribution
    • Laird, N. (1978), "Nonparametric Maximum Likelihood Estimation of a Mixing Distribution," Journal of the American Statistical Association, 73, 805-811.
    • (1978) Journal of the American Statistical Association , vol.73 , pp. 805-811
    • Laird, N.1
  • 26
    • 0007895414 scopus 로고
    • Smoothing the non-parametric estimate of a prior distribution by roughening: An empirical study
    • Laird, N. M., and Louis, T. A. (1991), "Smoothing the Non-Parametric Estimate of a Prior Distribution by Roughening: An Empirical Study," Computational Statistics and Data Analysis, 12, 27-38.
    • (1991) Computational Statistics and Data Analysis , vol.12 , pp. 27-38
    • Laird, N.M.1    Louis, T.A.2
  • 27
    • 0000042719 scopus 로고
    • Density estimation, stochastic processes and prior information
    • Ser. B
    • Leonard, T. (1978), "Density Estimation, Stochastic Processes and Prior Information," Journal of the Royal Statistical Society, Ser. B, 40, 113-132.
    • (1978) Journal of the Royal Statistical Society , vol.40 , pp. 113-132
    • Leonard, T.1
  • 28
    • 0000525359 scopus 로고
    • The geometry of mixture likelihoods: A general theory
    • Lindsay, B. G. (1983a), "The Geometry of Mixture Likelihoods: A General Theory," The Annals of Statistics, 11, 86-94.
    • (1983) The Annals of Statistics , vol.11 , pp. 86-94
    • Lindsay, B.G.1
  • 29
    • 0000525358 scopus 로고
    • The geometry of mixture likelihoods, part II: The exponential family
    • Lindsay, B. G. (1983b), "The Geometry of Mixture Likelihoods, Part II: The Exponential Family," The Annals of Statistics, 11, 783-792.
    • (1983) The Annals of Statistics , vol.11 , pp. 783-792
    • Lindsay, B.G.1
  • 30
    • 0003527944 scopus 로고
    • Hayward, CA: Institute of Mathematical Statistics/Alexandria, VA: American Statistical Association
    • Lindsay, B. G. (1995), Mixture Models: Theory, Geometry, and Applications, Hayward, CA: Institute of Mathematical Statistics/Alexandria, VA: American Statistical Association.
    • (1995) Mixture Models: Theory, Geometry, and Applications
    • Lindsay, B.G.1
  • 32
    • 0030329265 scopus 로고    scopus 로고
    • A smooth nonparametric estimate of a mixing distribution using mixtures of Gaussians
    • Magder, L. S., and Zeger, S. L. (1996), "A Smooth Nonparametric Estimate of a Mixing Distribution Using Mixtures of Gaussians," Journal of the American Statistical Association, 91, 1141-1151.
    • (1996) Journal of the American Statistical Association , vol.91 , pp. 1141-1151
    • Magder, L.S.1    Zeger, S.L.2
  • 33
    • 0033234633 scopus 로고    scopus 로고
    • Adaptive wavelet estimator for nonparametric density deconvolution
    • Pensky, M., and Vidakovic, B. (1999), "Adaptive Wavelet Estimator for Nonparametric Density Deconvolution," The Annals of Statistics, 27, 2033-2053.
    • (1999) The Annals of Statistics , vol.27 , pp. 2033-2053
    • Pensky, M.1    Vidakovic, B.2
  • 34
    • 0000738873 scopus 로고
    • On the estimation of a probability density function by the maximum penalized likelihood method
    • Silverman, B. W. (1982), "On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method," The Annals of Statistics, 10, 795-810.
    • (1982) The Annals of Statistics , vol.10 , pp. 795-810
    • Silverman, B.W.1
  • 36
    • 0002752852 scopus 로고
    • A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography
    • Ser. B
    • Silverman, B.W., Jones, M. C., Wilson, J. D., and Nychka, D.W. (1990), "A Smoothed EM Approach to Indirect Estimation Problems, With Particular Reference to Stereology and Emission Tomography," Journal of the Royal Statistical Society, Ser. B, 52, 271-324.
    • (1990) Journal of the Royal Statistical Society , vol.52 , pp. 271-324
    • Silverman, B.W.1    Jones, M.C.2    Wilson, J.D.3    Nychka, D.W.4
  • 37
    • 84972949113 scopus 로고
    • Deconvoluting kernel density estimators
    • Stefanski, L., and Carroll, R. J. (1990), "Deconvoluting Kernel Density Estimators," Statistics, 21, 169-184.
    • (1990) Statistics , vol.21 , pp. 169-184
    • Stefanski, L.1    Carroll, R.J.2
  • 38
    • 0037361758 scopus 로고    scopus 로고
    • Doubly smoothed EM algorithm for statistical inverse problems
    • Szkutnik, Z. (2003), "Doubly Smoothed EM Algorithm for Statistical Inverse Problems," Journal of the American Statistical Association, 98, 178-190.
    • (2003) Journal of the American Statistical Association , vol.98 , pp. 178-190
    • Szkutnik, Z.1
  • 42
    • 0002055609 scopus 로고
    • Fourier methods for estimating mixing densities and distributions
    • Zhang, C.-H. (1990), "Fourier Methods for Estimating Mixing Densities and Distributions," The Annals of Statistics, 18, 806-831.
    • (1990) The Annals of Statistics , vol.18 , pp. 806-831
    • Zhang, C.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.