메뉴 건너뛰기




Volumn 9, Issue 3, 2003, Pages 423-449

Optimal confidence bands for shape-restricted curves

Author keywords

Adaptivity; Concave; Convex; Isotonic; Kernel estimator; Local smoothness; Minimax bounds; Multiscale testing

Indexed keywords


EID: 3042530624     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1065444812     Document Type: Article
Times cited : (47)

References (23)
  • 1
    • 0000797991 scopus 로고
    • On some global measures of the deviations of density function estimates
    • Bickel, P.J. and Rosenblatt, M. (1973) On some global measures of the deviations of density function estimates. Ann. Statist., 1, 1071-1095.
    • (1973) Ann. Statist. , vol.1 , pp. 1071-1095
    • Bickel, P.J.1    Rosenblatt, M.2
  • 2
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • Brown, L.D. and Low, M.G. (1996) Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist., 24, 2384-2398.
    • (1996) Ann. Statist. , vol.24 , pp. 2384-2398
    • Brown, L.D.1    Low, M.G.2
  • 4
    • 0000467783 scopus 로고
    • One-sided inference about functionals of a density
    • Donoho, D.L. (1988) One-sided inference about functionals of a density. Ann. Statist., 16, 1390-1420.
    • (1988) Ann. Statist. , vol.16 , pp. 1390-1420
    • Donoho, D.L.1
  • 5
    • 0040040083 scopus 로고    scopus 로고
    • New goodness-of-fit tests and their application to nonparametric confidence sets
    • Dümbgen, L. (1998) New goodness-of-fit tests and their application to nonparametric confidence sets. Ann. Statist., 26, 288-314.
    • (1998) Ann. Statist. , vol.26 , pp. 288-314
    • Dümbgen, L.1
  • 7
    • 3042572506 scopus 로고    scopus 로고
    • Confidence bands for isotonic median curves using sign tests
    • To appear
    • Dümbgen, L. and Johns, R.B. (2003) Confidence bands for isotonic median curves using sign tests. J. Comput. Graph. Statist. To appear.
    • (2003) J. Comput. Graph. Statist.
    • Dümbgen, L.1    Johns, R.B.2
  • 8
    • 0035592604 scopus 로고    scopus 로고
    • Multiscale testing of qualitative hypotheses
    • Dümbgen, L. and Spokoiny, V.G. (2001) Multiscale testing of qualitative hypotheses. Ann. Statist., 29, 124-152.
    • (2001) Ann. Statist. , vol.29 , pp. 124-152
    • Dümbgen, L.1    Spokoiny, V.G.2
  • 9
    • 73149116074 scopus 로고
    • Confidence bands in nonparametric regression
    • Eubank, R.L. and Speckman, P.L. (1993) Confidence bands in nonparametric regression. J. Amer. Statist. Assoc., 88, 1287-1301.
    • (1993) J. Amer. Statist. Assoc. , vol.88 , pp. 1287-1301
    • Eubank, R.L.1    Speckman, P.L.2
  • 10
    • 0034354589 scopus 로고    scopus 로고
    • Simultaneous confidence bands and hypothesis testing in varying-coefficient models
    • Fan, J. and Zhang, W. (2000) Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scand. J. Statist., 27, 715-731.
    • (2000) Scand. J. Statist. , vol.27 , pp. 715-731
    • Fan, J.1    Zhang, W.2
  • 11
    • 0035633948 scopus 로고    scopus 로고
    • Generalized likelihood ratio statistics and Wilks phenomenon
    • Fan, J., Zhang, C. and Zhang, J. (2001) Generalized likelihood ratio statistics and Wilks phenomenon. Ann. Statist., 29, 153-193.
    • (2001) Ann. Statist. , vol.29 , pp. 153-193
    • Fan, J.1    Zhang, C.2    Zhang, J.3
  • 12
    • 0032094580 scopus 로고    scopus 로고
    • Asymptotic equivalence for nonparametric generalized linear models
    • Grama, I. and Nussbaum, M. (1998) Asymptotic equivalence for nonparametric generalized linear models. Probab. Theory Related Fields, 111, 167-214.
    • (1998) Probab. Theory Related Fields , vol.111 , pp. 167-214
    • Grama, I.1    Nussbaum, M.2
  • 13
    • 0000246894 scopus 로고
    • On confidence bands in nonparametric density estimation
    • Hall, P. and Titterington, D.M. (1988) On confidence bands in nonparametric density estimation. J. Multivariate Anal., 27, 228-254.
    • (1988) J. Multivariate Anal. , vol.27 , pp. 228-254
    • Hall, P.1    Titterington, D.M.2
  • 14
    • 0000958548 scopus 로고
    • Bootstrap simultaneous error bars for nonparametric regression
    • Härdle, W. and Marron, J.S. (1991) Bootstrap simultaneous error bars for nonparametric regression. Ann. Statist., 19, 778-796.
    • (1991) Ann. Statist. , vol.19 , pp. 778-796
    • Härdle, W.1    Marron, J.S.2
  • 16
    • 21844522284 scopus 로고
    • Finite-sample confidence envelopes for shape-restricted densities
    • Hengartner, N.W. and Stark, P.B. (1995) Finite-sample confidence envelopes for shape-restricted densities. Ann. Statist., 23, 525-550.
    • (1995) Ann. Statist. , vol.23 , pp. 525-550
    • Hengartner, N.W.1    Stark, P.B.2
  • 17
    • 0003058689 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives I
    • Ingster, Y.I. (1993a) Asymptotically minimax hypothesis testing for nonparametric alternatives I. Math. Methods Statist., 2, 85-114.
    • (1993) Math. Methods Statist. , vol.2 , pp. 85-114
    • Ingster, Y.I.1
  • 18
    • 0000484198 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives II
    • Ingster, Y.I. (1993b) Asymptotically minimax hypothesis testing for nonparametric alternatives II. Math. Methods Statist., 2, 171-189.
    • (1993) Math. Methods Statist. , vol.2 , pp. 171-189
    • Ingster, Y.I.1
  • 19
    • 0001047522 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives III
    • Ingster, Y.I. (1993c) Asymptotically minimax hypothesis testing for nonparametric alternatives III. Math. Methods Statist., 2, 249-268.
    • (1993) Math. Methods Statist. , vol.2 , pp. 249-268
    • Ingster, Y.I.1
  • 20
    • 0009387419 scopus 로고
    • A lower bound on the risks of non-parametric estimates of densities in the uniform metric
    • Khas'minskii, R.Z. (1978) A lower bound on the risks of non-parametric estimates of densities in the uniform metric. Theory Probab. Appl., 23, 794-798.
    • (1978) Theory Probab. Appl. , vol.23 , pp. 794-798
    • Khas'Minskii, R.Z.1
  • 22
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and white noise
    • Nussbaum, M. (1996) Asymptotic equivalence of density estimation and white noise. Ann. Statist., 24, 2399-2430.
    • (1996) Ann. Statist. , vol.24 , pp. 2399-2430
    • Nussbaum, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.