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Volumn 37, Issue 2, 2010, Pages 321-337

Density Estimation by Total Variation Penalized Likelihood Driven by the Sparsity ℓ1 Information Criterion

Author keywords

1 penalization; Convex programme; Dual block coordinate relaxation; Extreme value theory; Smoothing; Total variation; Universal penalty parameter

Indexed keywords


EID: 77953963579     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2009.00672.x     Document Type: Article
Times cited : (18)

References (50)
  • 1
    • 0000501656 scopus 로고
    • Information theory and an extension of the maximum likelihood principle
    • Petrov B N, Csaki F. eds, Akademiai Kiado, Budapest.
    • Akaike H. Information theory and an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory 1973, 267-281. Petrov B NCsaki F. eds, Akademiai Kiado, Budapest.
    • (1973) 2nd International Symposium on Information Theory , pp. 267-281
    • Akaike, H.1
  • 4
    • 0000013152 scopus 로고
    • On the statistical analysis of dirty pictures (with discussion)
    • Besag J. On the statistical analysis of dirty pictures (with discussion). J. Roy. Statist. Soc. Ser. B 1986, 48:192-236.
    • (1986) J. Roy. Statist. Soc. Ser. B , vol.48 , pp. 192-236
    • Besag, J.1
  • 6
    • 34250263445 scopus 로고
    • Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation
    • Craven P, Wahba G. Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 1979, 31:377-403.
    • (1979) Numer. Math. , vol.31 , pp. 377-403
    • Craven, P.1    Wahba, G.2
  • 7
    • 22944438248 scopus 로고    scopus 로고
    • Densities, spectral densities and modality
    • Davies P L, Kovac A. Densities, spectral densities and modality. Ann. Statist. 2004, 32:1093-1136.
    • (2004) Ann. Statist. , vol.32 , pp. 1093-1136
    • Davies, P.L.1    Kovac, A.2
  • 8
    • 0041958932 scopus 로고
    • Ideal spatial adaptation via wavelet shrinkage
    • Donoho D L, Johnstone I M. Ideal spatial adaptation via wavelet shrinkage. Biometrika 1994, 81:425-455.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 11
    • 0033233732 scopus 로고    scopus 로고
    • Optimal convergence rates for Good's nonparametric maximum likelihood density estimator
    • Eggermont P P B, LaRiccia V N. Optimal convergence rates for Good's nonparametric maximum likelihood density estimator. Ann. Statist. 1999, 27:1600-1615.
    • (1999) Ann. Statist. , vol.27 , pp. 1600-1615
    • Eggermont, P.P.B.1    LaRiccia, V.N.2
  • 12
    • 0032361278 scopus 로고    scopus 로고
    • Penalized regressions: the bridge versus the lasso
    • Fu W J. Penalized regressions: the bridge versus the lasso. J. Comput. Graph. Statist. 1998, 7:397-416.
    • (1998) J. Comput. Graph. Statist. , vol.7 , pp. 397-416
    • Fu, W.J.1
  • 13
    • 0021518209 scopus 로고
    • Stochastic relaxation. Gibbs distributions, and the Bayesian restoration of images
    • Geman S, Geman D. Stochastic relaxation. Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell 1984, 61:721-741.
    • (1984) IEEE Trans. Pattern Anal. Mach. Intell , vol.61 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 15
    • 0002142298 scopus 로고
    • A nonparametric roughness penalty for probability densities
    • Good I. A nonparametric roughness penalty for probability densities. Nature 1971, 229:29-30.
    • (1971) Nature , vol.229 , pp. 29-30
    • Good, I.1
  • 16
    • 0000451036 scopus 로고
    • Nonparametric roughness penalties for probability densities
    • Good I J, Gaskins R A. Nonparametric roughness penalties for probability densities. Biometrika 1971, 58:255-277.
    • (1971) Biometrika , vol.58 , pp. 255-277
    • Good, I.J.1    Gaskins, R.A.2
  • 17
    • 0018894430 scopus 로고
    • Confidence bands for a survival curve from censored data
    • Hall W J, Wellner J A. Confidence bands for a survival curve from censored data. Biometrika 1980, 67:133-143.
    • (1980) Biometrika , vol.67 , pp. 133-143
    • Hall, W.J.1    Wellner, J.A.2
  • 19
    • 0006380024 scopus 로고
    • Philatelic mixtures and multimodal densities
    • Izenman A J, Sommer C J. Philatelic mixtures and multimodal densities. J. Amer. Statist. Assoc. 1988, 83:941-953.
    • (1988) J. Amer. Statist. Assoc. , vol.83 , pp. 941-953
    • Izenman, A.J.1    Sommer, C.J.2
  • 21
  • 24
    • 84915425007 scopus 로고
    • Some comments on Cp
    • Mallows C L. Some comments on Cp. Technometrics 1973, 15:661-675.
    • (1973) Technometrics , vol.15 , pp. 661-675
    • Mallows, C.L.1
  • 25
    • 0031514745 scopus 로고    scopus 로고
    • Locally adaptive regression splines
    • Mammen E, van de Geer S. Locally adaptive regression splines. Ann. Statist. 1997, 25:387-413.
    • (1997) Ann. Statist. , vol.25 , pp. 387-413
    • Mammen, E.1    van de Geer, S.2
  • 26
    • 0001366850 scopus 로고
    • Exact mean integrated squared error
    • Marron J S, Wand M P. Exact mean integrated squared error. Ann. Statist. 1992, 20:712-736.
    • (1992) Ann. Statist. , vol.20 , pp. 712-736
    • Marron, J.S.1    Wand, M.P.2
  • 27
    • 0001047094 scopus 로고
    • Fast computation of fully automated log-density and log-hazard estimators
    • O'Sullivan F. Fast computation of fully automated log-density and log-hazard estimators. SIAM J. Sci. Statist. Comput. 1988, 9:363-379.
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 363-379
    • O'Sullivan, F.1
  • 28
    • 0040897887 scopus 로고    scopus 로고
    • On non-negative wavelet-based density estimators
    • Penev S, Dechevsky L. On non-negative wavelet-based density estimators. J. Nonparametr. Statist. 1997, 7:365-394.
    • (1997) J. Nonparametr. Statist. , vol.7 , pp. 365-394
    • Penev, S.1    Dechevsky, L.2
  • 29
    • 0031222253 scopus 로고    scopus 로고
    • Estimating the square root of a density via compactly supported wavelets
    • Pinheiro A, Vidakovic B. Estimating the square root of a density via compactly supported wavelets. Comput. Statist. Data Anal. 1997, 25:399-415.
    • (1997) Comput. Statist. Data Anal. , vol.25 , pp. 399-415
    • Pinheiro, A.1    Vidakovic, B.2
  • 30
    • 0036822492 scopus 로고    scopus 로고
    • Sensitivity and other properties of wavelet regression and density estimators
    • Renaud O. Sensitivity and other properties of wavelet regression and density estimators. Statist. Sinica 2002, 12:1275-1290.
    • (2002) Statist. Sinica , vol.12 , pp. 1275-1290
    • Renaud, O.1
  • 31
  • 32
    • 0003477772 scopus 로고
    • Wiley-Interscience, New-York, republished by Athena Scientific, Belmont, 1998
    • Rockafellar R T. Network flows and monotropic programming 1984, Wiley-Interscience, New-York, republished by Athena Scientific, Belmont, 1998
    • (1984) Network flows and monotropic programming
    • Rockafellar, R.T.1
  • 33
    • 0000795635 scopus 로고
    • Density estimation with confidence sets exemplified by superclusters and voids in the galaxies
    • Roeder K. Density estimation with confidence sets exemplified by superclusters and voids in the galaxies. J. Amer. Statist. Assoc. 1990, 85:617-624.
    • (1990) J. Amer. Statist. Assoc. , vol.85 , pp. 617-624
    • Roeder, K.1
  • 34
    • 70350501340 scopus 로고    scopus 로고
    • Adaptive posterior mode estimation of a sparse sequence for model selection
    • Sardy S. Adaptive posterior mode estimation of a sparse sequence for model selection. Scand. J. Statist. 2009, 36:577-601.
    • (2009) Scand. J. Statist. , vol.36 , pp. 577-601
    • Sardy, S.1
  • 35
    • 2142722218 scopus 로고    scopus 로고
    • On the statistical analysis of smoothing by maximizing dirty Markov random field posterior distributions
    • Sardy S, Tseng P. On the statistical analysis of smoothing by maximizing dirty Markov random field posterior distributions. J. Amer. Statist. Assoc. 2004, 99:191-204.
    • (2004) J. Amer. Statist. Assoc. , vol.99 , pp. 191-204
    • Sardy, S.1    Tseng, P.2
  • 36
    • 23044521122 scopus 로고    scopus 로고
    • Block coordinate relaxation methods for nonparametric wavelet denoising
    • Sardy S, Bruce A, Tseng P. Block coordinate relaxation methods for nonparametric wavelet denoising. J. Comput. Graph. Statist. 2000, 9:361-379.
    • (2000) J. Comput. Graph. Statist. , vol.9 , pp. 361-379
    • Sardy, S.1    Bruce, A.2    Tseng, P.3
  • 37
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • Schwarz G. Estimating the dimension of a model. Ann. Statist. 1978, 6:461-464.
    • (1978) Ann. Statist. , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 39
    • 0001268552 scopus 로고
    • A reliable data-based bandwidth selection method for kernel density estimation
    • Sheather S J, Jones M C. A reliable data-based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. Ser. B 1991, 53:683-690.
    • (1991) J. Roy. Statist. Soc. Ser. B , vol.53 , pp. 683-690
    • Sheather, S.J.1    Jones, M.C.2
  • 40
    • 0000738873 scopus 로고
    • On the estimation of a probability density function by the maximum penalized likelihood method
    • Silverman B W. On the estimation of a probability density function by the maximum penalized likelihood method. Ann. Statist. 1982, 10:795-810.
    • (1982) Ann. Statist. , vol.10 , pp. 795-810
    • Silverman, B.W.1
  • 43
    • 0000629975 scopus 로고
    • Cross-validatory choice and assessment of statistical predictions (with discussion)
    • Stone M. Cross-validatory choice and assessment of statistical predictions (with discussion). J. Roy. Statist. Soc. Ser. B 1974, 36:111-147.
    • (1974) J. Roy. Statist. Soc. Ser. B , vol.36 , pp. 111-147
    • Stone, M.1
  • 44
    • 0000645875 scopus 로고
    • Large sample inference for logspline model
    • Stone C J. Large sample inference for logspline model. Ann. Statist. 1990, 18:717-741.
    • (1990) Ann. Statist. , vol.18 , pp. 717-741
    • Stone, C.J.1
  • 45
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • Tibshirani R. Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 1996, 58:267-288.
    • (1996) J. Roy. Statist. Soc. Ser. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 46
    • 0001300994 scopus 로고
    • Solution of incorrectly formulated problems and the regularization method
    • Tikhonov A N. Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. 1963, 4:1035-1038.
    • (1963) Soviet Math. Dokl. , vol.4 , pp. 1035-1038
    • Tikhonov, A.N.1
  • 47
    • 0035533631 scopus 로고    scopus 로고
    • Convergence of block coordinate descent method for nondifferentiable minimization
    • Tseng P. Convergence of block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 2001, 109:475-494.
    • (2001) J. Optim. Theory Appl. , vol.109 , pp. 475-494
    • Tseng, P.1
  • 49
    • 0003466536 scopus 로고
    • Society for Industrial and Applied Mathematics, Philadelphia, PA
    • Wahba G. Spline models for observational data 1990, Society for Industrial and Applied Mathematics, Philadelphia, PA
    • (1990) Spline models for observational data
    • Wahba, G.1


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