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Volumn 51, Issue 12, 2007, Pages 5622-5634

Bivariate density estimation using BV regularisation

Author keywords

Density estimation; Modality; Regularisation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DATA REDUCTION; PROBLEM SOLVING;

EID: 34547148535     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.04.019     Document Type: Article
Times cited : (9)

References (53)
  • 1
    • 0038578256 scopus 로고    scopus 로고
    • Simple estimation of the mode of a multivariate density
    • Abraham C., Biau G., and Cadre B. Simple estimation of the mode of a multivariate density. Canad. J. Statist. 31 (2003) 23-34
    • (2003) Canad. J. Statist. , vol.31 , pp. 23-34
    • Abraham, C.1    Biau, G.2    Cadre, B.3
  • 3
    • 34547175973 scopus 로고    scopus 로고
    • Aurenhammer, F., Klein, R., 2000. Handbook of Computational Geometry. Elsevier, Amsterdam, pp. 201-290 (Chapter 5).
  • 4
    • 0001741790 scopus 로고
    • A look at some data on the Old Faithful Geyser
    • Azzalini A., and Bowman A.W. A look at some data on the Old Faithful Geyser. Applied Statistics 39 (1990) 357-365
    • (1990) Applied Statistics , vol.39 , pp. 357-365
    • Azzalini, A.1    Bowman, A.W.2
  • 7
    • 0035608644 scopus 로고    scopus 로고
    • Local extremes, runs, strings and multiresolution (with discussion)
    • Davies P.L., and Kovac A. Local extremes, runs, strings and multiresolution (with discussion). Ann. Statist. 29 (2001) 1-65
    • (2001) Ann. Statist. , vol.29 , pp. 1-65
    • Davies, P.L.1    Kovac, A.2
  • 8
    • 22944438248 scopus 로고    scopus 로고
    • Densities, spectral densities and modality
    • Davies P.L., and Kovac A. Densities, spectral densities and modality. Ann. Statist. 32 3 (2004) 1093-1136
    • (2004) Ann. Statist. , vol.32 , Issue.3 , pp. 1093-1136
    • Davies, P.L.1    Kovac, A.2
  • 9
    • 34547188375 scopus 로고    scopus 로고
    • Davies, P.L., Gather, U., Weinert, H., 2006. Nonparametric regression as an example of model choice. Technical Report 24/06, Sonderforschungsbereich 475, Fachbereich Statistik, University of Dortmund, Germany.
  • 10
    • 84984346713 scopus 로고
    • Recursive estimation of the mode of a multivariate density
    • Devroye L. Recursive estimation of the mode of a multivariate density. Canad. J. Statist. 7 (1979) 159-167
    • (1979) Canad. J. Statist. , vol.7 , pp. 159-167
    • Devroye, L.1
  • 12
    • 0001618486 scopus 로고
    • Optimum kernel estimators of the mode
    • Eddy W. Optimum kernel estimators of the mode. Ann. Statist. 8 (1980) 870-882
    • (1980) Ann. Statist. , vol.8 , pp. 870-882
    • Eddy, W.1
  • 14
    • 25444532788 scopus 로고    scopus 로고
    • Flexible smoothing with b-splines and penalties
    • Eilers P., and Marx B. Flexible smoothing with b-splines and penalties. Statist. Sci. 11 (1996) 89-102
    • (1996) Statist. Sci. , vol.11 , pp. 89-102
    • Eilers, P.1    Marx, B.2
  • 18
    • 0000546952 scopus 로고    scopus 로고
    • Nonparametric estimation of the mode of a distribution of random curves
    • Gasser T., Hall P., and Presnell B. Nonparametric estimation of the mode of a distribution of random curves. J. Roy. Statist. Soc. 60 (1998) 681-691
    • (1998) J. Roy. Statist. Soc. , vol.60 , pp. 681-691
    • Gasser, T.1    Hall, P.2    Presnell, B.3
  • 19
    • 84950634092 scopus 로고
    • Density estimating and bump-hunting by the penalizedlikelihood method exemplified by scattering and meteorite data
    • Good I., and Gaskins R. Density estimating and bump-hunting by the penalizedlikelihood method exemplified by scattering and meteorite data. J. Amer. Statist. Assoc. 75 (1980) 42-73
    • (1980) J. Amer. Statist. Assoc. , vol.75 , pp. 42-73
    • Good, I.1    Gaskins, R.2
  • 20
    • 34547189401 scopus 로고    scopus 로고
    • Grasmair, M., 2006. The equivalence of the taut string algorithm and bv-regularization. J. Math. Imaging Vision.
  • 22
    • 21844522284 scopus 로고
    • Finite-sample confidence envelopes for shape-restricted densities
    • Hengartner N., and Stark P. Finite-sample confidence envelopes for shape-restricted densities. Ann. Statist. 23 (1995) 525-550
    • (1995) Ann. Statist. , vol.23 , pp. 525-550
    • Hengartner, N.1    Stark, P.2
  • 23
    • 3042687336 scopus 로고    scopus 로고
    • Rates on consistency for nonparametric estimation of the mode in absence of smoothness assumptions
    • Herrmann E., and Ziegler K. Rates on consistency for nonparametric estimation of the mode in absence of smoothness assumptions. Statist. Probab. Lett. 68 (2004) 359-368
    • (2004) Statist. Probab. Lett. , vol.68 , pp. 359-368
    • Herrmann, E.1    Ziegler, K.2
  • 24
    • 0242526898 scopus 로고    scopus 로고
    • Tube methods for bv regularization
    • Hinterberger W., et al. Tube methods for bv regularization. J. Math. Imaging Vision 19 (2003) 219-235
    • (2003) J. Math. Imaging Vision , vol.19 , pp. 219-235
    • Hinterberger, W.1
  • 25
    • 0346083990 scopus 로고    scopus 로고
    • Kernel estimators of general radon-nikodym derivatives
    • Jacob P., and Oliveira P. Kernel estimators of general radon-nikodym derivatives. Statistics 30 (1997) 25-46
    • (1997) Statistics , vol.30 , pp. 25-46
    • Jacob, P.1    Oliveira, P.2
  • 26
    • 25444451915 scopus 로고    scopus 로고
    • Nonparametric density estimation and clustering in astronomical sky surveys
    • Jang W. Nonparametric density estimation and clustering in astronomical sky surveys. Comput. Statist. Data Anal. 50 (2006) 760-774
    • (2006) Comput. Statist. Data Anal. , vol.50 , pp. 760-774
    • Jang, W.1
  • 27
    • 34247366813 scopus 로고    scopus 로고
    • Smooth functions and local extreme values
    • Kovac A. Smooth functions and local extreme values. Comput. Statist. Data Anal. 51 (2007) 5156-5171
    • (2007) Comput. Statist. Data Anal. , vol.51 , pp. 5156-5171
    • Kovac, A.1
  • 28
    • 0001308460 scopus 로고
    • On qualitative smoothness of kernel density estimators
    • Mammen E. On qualitative smoothness of kernel density estimators. Statistics 26 (1995) 253-267
    • (1995) Statistics , vol.26 , pp. 253-267
    • Mammen, E.1
  • 29
    • 0031514745 scopus 로고    scopus 로고
    • Locally adaptive regression splines
    • Mammen E., and van de Geer S. Locally adaptive regression splines. Ann. Statist. 25 (1997) 387-413
    • (1997) Ann. Statist. , vol.25 , pp. 387-413
    • Mammen, E.1    van de Geer, S.2
  • 30
    • 0002137778 scopus 로고
    • The mode tree: a tool for visualization of nonparametric density features
    • Minotte M.C., and Scott D.W. The mode tree: a tool for visualization of nonparametric density features. J. Comput. Graphical Statist. 2 (1993) 51-68
    • (1993) J. Comput. Graphical Statist. , vol.2 , pp. 51-68
    • Minotte, M.C.1    Scott, D.W.2
  • 31
    • 0000371878 scopus 로고
    • Excess mass estimates and tests for multimodality
    • Müller D.W., and Sawitzki G. Excess mass estimates and tests for multimodality. J. Amer. Statist. Assoc. 86 415 (1991) 738-746
    • (1991) J. Amer. Statist. Assoc. , vol.86 , Issue.415 , pp. 738-746
    • Müller, D.W.1    Sawitzki, G.2
  • 32
    • 0000570384 scopus 로고
    • On estimating regression
    • Nadaraya E.A. On estimating regression. Theory Probab. Appl. 10 (1964) 186-190
    • (1964) Theory Probab. Appl. , vol.10 , pp. 186-190
    • Nadaraya, E.A.1
  • 33
    • 0001048922 scopus 로고
    • Practical performance of several data-driven bandwidth selectors (with discussion)
    • Park B.-U., and Turlach B. Practical performance of several data-driven bandwidth selectors (with discussion). Comput. Statist. 7 (1992) 251-285
    • (1992) Comput. Statist. , vol.7 , pp. 251-285
    • Park, B.-U.1    Turlach, B.2
  • 34
    • 0001473437 scopus 로고
    • On estimation of a probability density function and mode
    • Parzen E. On estimation of a probability density function and mode. Ann. Math. Statist. 33 (1962) 1065-1076
    • (1962) Ann. Math. Statist. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 35
    • 0002491164 scopus 로고
    • Density estimation under qualitative assumptions inhigher dimensions
    • Polonik W. Density estimation under qualitative assumptions inhigher dimensions. J. Mulitivariate Anal. 55 (1995) 61-81
    • (1995) J. Mulitivariate Anal. , vol.55 , pp. 61-81
    • Polonik, W.1
  • 36
    • 0001030653 scopus 로고
    • Measuring mass concentrations and estimating density contour clusters-an excess mass approach
    • Polonik W. Measuring mass concentrations and estimating density contour clusters-an excess mass approach. Ann. Statist 23 (1995) 855-881
    • (1995) Ann. Statist , vol.23 , pp. 855-881
    • Polonik, W.1
  • 37
    • 0033236910 scopus 로고    scopus 로고
    • Concentration and goodness of fit in higherdimensions: (aymptotically) distribution-free methods
    • Polonik W. Concentration and goodness of fit in higherdimensions: (aymptotically) distribution-free methods. Ann. Statist. 27 (1999) 1210-1229
    • (1999) Ann. Statist. , vol.27 , pp. 1210-1229
    • Polonik, W.1
  • 38
    • 0034361296 scopus 로고    scopus 로고
    • Adaptive weights smoothing with applications to image resoration
    • Polzehl J., and Spokoiny V. Adaptive weights smoothing with applications to image resoration. J. Roy. Statist. Soc. Ser. B. 62 (2000) 335-354
    • (2000) J. Roy. Statist. Soc. Ser. B. , vol.62 , pp. 335-354
    • Polzehl, J.1    Spokoiny, V.2
  • 39
    • 34547181563 scopus 로고    scopus 로고
    • Pöschl, C., Scherzer, O., 2006. Characterization of minimizers of convex regularization functionals. Technical Report 42, Institute for Computer Science, University Innsbruck.
  • 40
    • 18244378520 scopus 로고    scopus 로고
    • On bayesian analysis of mixtures with an unknown number of components (with discussion)
    • Richardson S., and Green P. On bayesian analysis of mixtures with an unknown number of components (with discussion). J. Roy. Statist. Soc. 59 (1997) 731-792
    • (1997) J. Roy. Statist. Soc. , vol.59 , pp. 731-792
    • Richardson, S.1    Green, P.2
  • 41
    • 0014460022 scopus 로고
    • Thermal and seismic indications of old faithful geyser's inner workings
    • Rinehart J.S. Thermal and seismic indications of old faithful geyser's inner workings. J. Geophys. Res. 74 (1969) 566
    • (1969) J. Geophys. Res. , vol.74 , pp. 566
    • Rinehart, J.S.1
  • 42
    • 21744460005 scopus 로고    scopus 로고
    • Practical Bayesian density estimation using mixtures of normals
    • Roeder K., and Wasserman L. Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92 439 (1997) 894-902
    • (1997) J. Amer. Statist. Assoc. , vol.92 , Issue.439 , pp. 894-902
    • Roeder, K.1    Wasserman, L.2
  • 43
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • Rudin L., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 44
    • 0030327572 scopus 로고    scopus 로고
    • On locally adaptive density estimation
    • Sain S., and Scott D. On locally adaptive density estimation. J. Amer. Statist. Assoc. 91 (1996) 1525-1534
    • (1996) J. Amer. Statist. Assoc. , vol.91 , pp. 1525-1534
    • Sain, S.1    Scott, D.2
  • 45
    • 23944465533 scopus 로고    scopus 로고
    • Taut-string algorithm and regularization programs with g-norm data fit
    • Scherzer O. Taut-string algorithm and regularization programs with g-norm data fit. J. Math. Imaging Vision 23 2 (2005) 135-143
    • (2005) J. Math. Imaging Vision , vol.23 , Issue.2 , pp. 135-143
    • Scherzer, O.1
  • 49
    • 13244274395 scopus 로고    scopus 로고
    • On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and sides
    • Steidl G., Weickert J., Brox J., Mrazek P., and Welk M. On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and sides. SIAM J. Numer. Anal. 42 2 (2004) 686-713
    • (2004) SIAM J. Numer. Anal. , vol.42 , Issue.2 , pp. 686-713
    • Steidl, G.1    Weickert, J.2    Brox, J.3    Mrazek, P.4    Welk, M.5
  • 51
    • 0000888197 scopus 로고    scopus 로고
    • A note on density mode estimation
    • Vieu P. A note on density mode estimation. Statist. Probab. Lett. 26 (1996) 297-307
    • (1996) Statist. Probab. Lett. , vol.26 , pp. 297-307
    • Vieu, P.1
  • 53
    • 0001762426 scopus 로고
    • Smooth regression analysis
    • Watson G.S. Smooth regression analysis. Sankhyā 26 (1964) 101-116
    • (1964) Sankhyā , vol.26 , pp. 101-116
    • Watson, G.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.