메뉴 건너뛰기




Volumn 8, Issue 4, 2002, Pages 423-449

Nonlinear kernel density estimation for binned data: Convergence in entropy

Author keywords

Binned data; Density estimation; Kernel estimation; Logarithmic sobolev inequality; Transportation

Indexed keywords


EID: 10844295401     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (15)

References (27)
  • 2
    • 0000061719 scopus 로고
    • Entropy and the central limit theorem
    • Barron, A.R. (1986) Entropy and the central limit theorem. Ann. Probab., 14, 336-342.
    • (1986) Ann. Probab. , vol.14 , pp. 336-342
    • Barron, A.R.1
  • 3
    • 0000404653 scopus 로고
    • Approximation of density functions by sequences of exponential families
    • Barron, A.R. and Sheu, C.H. (1991) Approximation of density functions by sequences of exponential families. Ann. Statist., 19, 1347-1369.
    • (1991) Ann. Statist. , vol.19 , pp. 1347-1369
    • Barron, A.R.1    Sheu, C.H.2
  • 4
    • 0003064476 scopus 로고
    • Spline transformations: Three new diagnostic aids for the statistical data-analyst
    • Boneva, L.I., Kendall, D.G. and Stefanov, I. (1971) Spline transformations: Three new diagnostic aids for the statistical data-analyst (with discussion). J. Roy. Statist. Soc. Ser. B, 33, 1-70.
    • (1971) J. Roy. Statist. Soc. Ser. B , vol.33 , pp. 1-70
    • Boneva, L.I.1    Kendall, D.G.2    Stefanov, I.3
  • 5
    • 0001245944 scopus 로고
    • An alternative method of cross validation for the smoothing of density estimates
    • Bowman, A.W. (1984) An alternative method of cross validation for the smoothing of density estimates. Biometrika, 71, 353-360.
    • (1984) Biometrika , vol.71 , pp. 353-360
    • Bowman, A.W.1
  • 6
    • 0000860574 scopus 로고
    • Entropy production by block variable summation and central limit theorems
    • Carlen, E.A. and Soffer, A. (1991) Entropy production by block variable summation and central limit theorems. Comm. Math. Phys., 140, 339-371.
    • (1991) Comm. Math. Phys. , vol.140 , pp. 339-371
    • Carlen, E.A.1    Soffer, A.2
  • 8
    • 38249018162 scopus 로고
    • Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models
    • Deuschel, J.-D. and Stroock, D.W. (1990) Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models. J. Funct. Anal., 92, 30-48.
    • (1990) J. Funct. Anal. , vol.92 , pp. 30-48
    • Deuschel, J.-D.1    Stroock, D.W.2
  • 10
    • 0001429116 scopus 로고
    • Logarithmic Sobolev inequalities
    • Gross, L. (1975) Logarithmic Sobolev inequalities. Amer. J. Math., 97, 1061-1083.
    • (1975) Amer. J. Math. , vol.97 , pp. 1061-1083
    • Gross, L.1
  • 11
    • 0002236459 scopus 로고
    • Logarithmic Sobolev inequalities and contractivity properties of semigroups
    • G. Dell'Antonio and U. Mosco (eds) Lecture Notes in Math. 1563 . Berlin: Springer-Verlag
    • Gross, L. (1993) Logarithmic Sobolev inequalities and contractivity properties of semigroups. In G. Dell'Antonio and U. Mosco (eds), Dirichlet Forms (Varenna, 1992), Lecture Notes in Math. 1563, pp. 54-88. Berlin: Springer-Verlag.
    • (1993) Dirichlet Forms (Varenna, 1992) , pp. 54-88
    • Gross, L.1
  • 12
    • 0003097597 scopus 로고
    • Smoothing by weighted averaging of rounded points
    • Härdle, W.K. and Scott, D.W. (1992) Smoothing by weighted averaging of rounded points. Comput. Statist., 7, 97-128.
    • (1992) Comput. Statist. , vol.7 , pp. 97-128
    • Härdle, W.K.1    Scott, D.W.2
  • 15
    • 0042785054 scopus 로고    scopus 로고
    • Logspline density estimation for binned data
    • Koo, J.Y. and Kooperberg, C. (2000) Logspline density estimation for binned data. Statist. Probab. Lett., 46, 133-147.
    • (2000) Statist. Probab. Lett. , vol.46 , pp. 133-147
    • Koo, J.Y.1    Kooperberg, C.2
  • 17
    • 0030532989 scopus 로고    scopus 로고
    • The bias-optimized frequency polygon
    • Minnotte, M.C. (1996) The bias-optimized frequency polygon. Comput. Statist., 11, 35-48.
    • (1996) Comput. Statist. , vol.11 , pp. 35-48
    • Minnotte, M.C.1
  • 18
    • 0032366181 scopus 로고    scopus 로고
    • Achieving high-order convergence rates for density estimation with binned data
    • Minnotte, M.C. (1998) Achieving high-order convergence rates for density estimation with binned data. J. Amer. Statist. Assoc., 93, 663-672.
    • (1998) J. Amer. Statist. Assoc. , vol.93 , pp. 663-672
    • Minnotte, M.C.1
  • 19
    • 0001559554 scopus 로고    scopus 로고
    • Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
    • Otto, F. and Villani, C. (2000) Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal., 173, 361-400.
    • (2000) J. Funct. Anal. , vol.173 , pp. 361-400
    • Otto, F.1    Villani, C.2
  • 20
    • 84968517521 scopus 로고
    • Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators
    • Rothaus, O.S. (1980) Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators. J. Funct. Anal., 39, 42-56.
    • (1980) J. Funct. Anal. , vol.39 , pp. 42-56
    • Rothaus, O.S.1
  • 22
    • 0001268552 scopus 로고
    • A reliable data-based bandwidth selection method for kernel density estimation
    • Sheather, S.J. and Jones, M.C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. Ser. B, 53, 683-690.
    • (1991) J. Roy. Statist. Soc. Ser. B , vol.53 , pp. 683-690
    • Sheather, S.J.1    Jones, M.C.2
  • 23
    • 0031484203 scopus 로고    scopus 로고
    • Polynomial splines and their tensor products in extended linear modelling
    • Stone, C.J., Hansen, M.H., Kooperberg, C. and Truong, Y.K. (1997) Polynomial splines and their tensor products in extended linear modelling. Ann. Statist., 25, 1454-1470.
    • (1997) Ann. Statist. , vol.25 , pp. 1454-1470
    • Stone, C.J.1    Hansen, M.H.2    Kooperberg, C.3    Truong, Y.K.4
  • 24
    • 0030551055 scopus 로고    scopus 로고
    • Transportation cost for Gaussian and other product measures
    • Talagrand, M. (1996) Transportation cost for Gaussian and other product measures. Geom. Funct. Anal., 6, 587-600.
    • (1996) Geom. Funct. Anal. , vol.6 , pp. 587-600
    • Talagrand, M.1
  • 25
    • 84909718035 scopus 로고
    • Kernel-based density estimation using censored, truncated or grouped data
    • Titterington, D.M. (1983) Kernel-based density estimation using censored, truncated or grouped data. Comm. Statist. Theory Methods, 12, 2151-2167.
    • (1983) Comm. Statist. Theory Methods , vol.12 , pp. 2151-2167
    • Titterington, D.M.1
  • 26
    • 0018659851 scopus 로고
    • Smooth pycnophylactic interpolation for geographical regions
    • Tobler, W.R. (1979) Smooth pycnophylactic interpolation for geographical regions. J. Amer. Statist. Assoc., 74, 519-536.
    • (1979) J. Amer. Statist. Assoc. , vol.74 , pp. 519-536
    • Tobler, W.R.1
  • 27
    • 0004236801 scopus 로고
    • London: Chapman & Hall. Received July 1999 and revised August 2001 and February 2002
    • Wand, M.P. and Jones, M.C. (1995) Kernel Smoothing. London: Chapman & Hall. Received July 1999 and revised August 2001 and February 2002
    • (1995) Kernel Smoothing
    • Wand, M.P.1    Jones, M.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.