메뉴 건너뛰기




Volumn 12, Issue 3, 2000, Pages 417-445

Minimax Kernels for nonparametric curve estimation

Author keywords

Derivative estimation; Gaussian based kernel; Higher order kernel; Kernel density estimation; Minimax kernel; Optimal kernel

Indexed keywords


EID: 0038780148     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250008832816     Document Type: Article
Times cited : (6)

References (25)
  • 1
    • 0346220321 scopus 로고
    • On asymptotic minimaxity of the adaptive kernel estimate of a density function
    • Bretagnolle, J. and Mielniczuk, J. (1989) On asymptotic minimaxity of the adaptive kernel estimate of a density function. Ann. Inst. Hen. Poin., 25(2), 143-152.
    • (1989) Ann. Inst. Hen. Poin. , vol.25 , Issue.2 , pp. 143-152
    • Bretagnolle, J.1    Mielniczuk, J.2
  • 3
    • 0000251164 scopus 로고
    • Geometrizing rate of convergence II
    • Donoho, D. L. and Liu, R. C. (1991a) Geometrizing rate of convergence II. Ann. Statist., 19, 633-667.
    • (1991) Ann. Statist. , vol.19 , pp. 633-667
    • Donoho, D.L.1    Liu, R.C.2
  • 4
    • 0000251164 scopus 로고
    • Geometrizing rate of convergence III
    • Donoho, D. L. and Liu, R. C. (1991b) Geometrizing rate of convergence III. Ann. Statist., 19, 668-701.
    • (1991) Ann. Statist. , vol.19 , pp. 668-701
    • Donoho, D.L.1    Liu, R.C.2
  • 5
    • 0000665083 scopus 로고
    • Nonparametric estimation of a multidimensional probability density
    • Epanechnikov, V.A. (1969) Nonparametric estimation of a multidimensional probability density. Theory Probab. Appl., 14, 153-158.
    • (1969) Theory Probab. Appl. , vol.14 , pp. 153-158
    • Epanechnikov, V.A.1
  • 6
    • 3042869574 scopus 로고
    • Local linear regression smoothers and their minimax efficiency
    • Fan, J. (1993) Local linear regression smoothers and their minimax efficiency. Ann. Statist., 21, 196-216.
    • (1993) Ann. Statist. , vol.21 , pp. 196-216
    • Fan, J.1
  • 7
    • 38249013982 scopus 로고
    • Bias correction and higher-order kernel functions
    • Fan, J. and Hu, T. C. (1992) Bias correction and higher-order kernel functions, Statist. Prob. Lett., 13, 235-243.
    • (1992) Statist. Prob. Lett. , vol.13 , pp. 235-243
    • Fan, J.1    Hu, T.C.2
  • 10
    • 0001257368 scopus 로고
    • Estimating regression functions and their derivatives by the kernel method
    • Gasser, Th. and Müller, H. G. (1984) Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist., 11, 171-185.
    • (1984) Scand. J. Statist. , vol.11 , pp. 171-185
    • Gasser, Th.1    Müller, H.G.2
  • 12
    • 84961472858 scopus 로고
    • On the optimality of a class of polynomial kernel functions
    • Dec.
    • Granovsky, B. L. and Müller, H. G. (1989) On the optimality of a class of polynomial kernel functions. Statist., Dec., 7, 301-312.
    • (1989) Statist. , vol.7 , pp. 301-312
    • Granovsky, B.L.1    Müller, H.G.2
  • 13
    • 0000587756 scopus 로고
    • Optimizing kernel methods: A unifying variational principle
    • Granovsky, B. L. and Müller, H. G. (1991) Optimizing kernel methods: a unifying variational principle. Internat. Statist. Rev., 59(3), 373-388.
    • (1991) Internat. Statist. Rev. , vol.59 , Issue.3 , pp. 373-388
    • Granovsky, B.L.1    Müller, H.G.2
  • 14
    • 0010810583 scopus 로고
    • Bandwidth choice for density derivative
    • Hardle, W., Marron, J. S. and Wand, M. P. (1990) Bandwidth choice for density derivative, J. Roy. Statist. Soc. B, 52(1), 223-232.
    • (1990) J. Roy. Statist. Soc. B , vol.52 , Issue.1 , pp. 223-232
    • Hardle, W.1    Marron, J.S.2    Wand, M.P.3
  • 16
    • 84961478474 scopus 로고
    • A note on kernels fulfilling certain moment conditions
    • Madrid 1983
    • Mammitzsch (1983) A note on kernels fulfilling certain moment conditions. In: Proc. of 44th Session of the Int. Statist. Inst. (Madrid 1983), I, 31-34.
    • (1983) Proc. of 44th Session of the Int. Statist. Inst. , vol.1 , pp. 31-34
    • Mammitzsch1
  • 17
    • 0009421771 scopus 로고
    • On the asymptotically optimal solution within a certain class of kernel type estimators
    • Dec.
    • Mammitzsch (1984) On the asymptotically optimal solution within a certain class of kernel type estimators. Statist., Dec., 2, 247-255.
    • (1984) Statist. , vol.2 , pp. 247-255
    • Mammitzsch1
  • 18
    • 0000052498 scopus 로고
    • Smooth optimum kernel estimators for density, regression curves and modes
    • Müller, H. G. (1984) Smooth optimum kernel estimators for density, regression curves and modes. Ann. Statist., 12, 766-774.
    • (1984) Ann. Statist. , vol.12 , pp. 766-774
    • Müller, H.G.1
  • 19
    • 0000423464 scopus 로고
    • Smooth optimum kernel estimators near endpoints
    • Müller, H. G. (1991) Smooth optimum kernel estimators near endpoints. Biometrika, 78, 521-530.
    • (1991) Biometrika , vol.78 , pp. 521-530
    • Müller, H.G.1
  • 20
    • 84947934780 scopus 로고
    • An effective bandwidth selector for local least squares regression
    • Ruppert, D., Sheather, S. J. and Wand, M. P. (1995) An effective bandwidth selector for local least squares regression, J. Amer. Statist. Assoc., 90, 1257-1270.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 1257-1270
    • Ruppert, D.1    Sheather, S.J.2    Wand, M.P.3
  • 21
    • 0007329673 scopus 로고
    • Asymptotically optimum kernels for density estimation at a point
    • Sacks, J. and Ylvisaker, D. (1981) Asymptotically optimum kernels for density estimation at a point. Ann. Statist., 9, 334-346.
    • (1981) Ann. Statist. , vol.9 , pp. 334-346
    • Sacks, J.1    Ylvisaker, D.2
  • 22
    • 0000735458 scopus 로고
    • Linear estimation for approximately linear models
    • Sacks, J. and Ylvisaker, D. (1978) Linear estimation for approximately linear models. Ann. Statist., 6, 1122-1137.
    • (1978) Ann. Statist. , vol.6 , pp. 1122-1137
    • Sacks, J.1    Ylvisaker, D.2
  • 23
    • 38249005286 scopus 로고
    • On nonparametric regression with higher-order kernels
    • Schucany, W. R. (1989) On nonparametric regression with higher-order kernels. J. Statist. Plann. Inferences, 23, 145-151.
    • (1989) J. Statist. Plann. Inferences , vol.23 , pp. 145-151
    • Schucany, W.R.1
  • 25
    • 84988097431 scopus 로고
    • Gaussian-based kernels
    • Wand, M. P. and Schucany (1990) Gaussian-based kernels, Candi. J. Statist., 18(3), 197-204.
    • (1990) Candi. J. Statist. , vol.18 , Issue.3 , pp. 197-204
    • Wand, M.P.1    Schucany2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.