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Volumn 123, Issue 2, 2004, Pages 225-242

Minimax exact constant in sup-norm for nonparametric regression with random design

Author keywords

Minimax exact constant; Minimax risk; Nonparametric regression; Uniform norm

Indexed keywords


EID: 2142828480     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(03)00154-X     Document Type: Article
Times cited : (12)

References (11)
  • 1
    • 21344480943 scopus 로고
    • Asymptotic minimax risk for sup-norm loss: Solution via optimal recovery
    • Donoho D. Asymptotic minimax risk for sup-norm loss: solution via optimal recovery Probab. Theory Related Fields 99 1994 145-170
    • (1994) Probab. Theory Related Fields , vol.99 , pp. 145-170
    • Donoho, D.1
  • 4
    • 0009216977 scopus 로고
    • Bounds for the risks of nonparametric regression estimates
    • Ibragimov I.A. Has'minskii R.Z. Bounds for the risks of nonparametric regression estimates Theory Probab. Appl. 27 1982 84-99
    • (1982) Theory Probab. Appl. , vol.27 , pp. 84-99
    • Ibragimov, I.A.1    Has'minskii, R.Z.2
  • 5
    • 0000348715 scopus 로고
    • Asymptotically minimax regression estimator in the uniform norm up to the exact constant
    • Korostelev A.P. Asymptotically minimax regression estimator in the uniform norm up to the exact constant Theory Probab. Appl. 38 1993 737-743
    • (1993) Theory Probab. Appl. , vol.38 , pp. 737-743
    • Korostelev, A.P.1
  • 6
    • 0042112381 scopus 로고    scopus 로고
    • The asymptotic minimax constant for sup-norm loss in nonparametric density estimation
    • Korostelev A.P. Nussbaum M. The asymptotic minimax constant for sup-norm loss in nonparametric density estimation Bernoulli 5 1999 1099-1118
    • (1999) Bernoulli , vol.5 , pp. 1099-1118
    • Korostelev, A.P.1    Nussbaum, M.2
  • 7
    • 0001633551 scopus 로고    scopus 로고
    • On the solution of an optimal recovery problem and its applications in nonparametric regression
    • Leonov S.L. On the solution of an optimal recovery problem and its applications in nonparametric regression Math. Methods Statist. 4 1997 476-490
    • (1997) Math. Methods Statist. , vol.4 , pp. 476-490
    • Leonov, S.L.1
  • 8
    • 0007320371 scopus 로고
    • On problems of adaptive estimation in white noise
    • Lepski O.V. On problems of adaptive estimation in white noise Adv. Soviet Math. 12 1992 87-106
    • (1992) Adv. Soviet Math. , vol.12 , pp. 87-106
    • Lepski, O.V.1
  • 9
    • 0034399225 scopus 로고    scopus 로고
    • Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point
    • Lepski O.V. Tsybakov A.B. Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point Probab. Theory Related Fields 117 2000 17-48
    • (2000) Probab. Theory Related Fields , vol.117 , pp. 17-48
    • Lepski, O.V.1    Tsybakov, A.B.2
  • 10
    • 0000439527 scopus 로고
    • Optimal global rates of convergence for nonparametric regression
    • Stone C.J. Optimal global rates of convergence for nonparametric regression Ann. Statist. 13 1982 1040-1053
    • (1982) Ann. Statist. , vol.13 , pp. 1040-1053
    • Stone, C.J.1
  • 11
    • 2142785414 scopus 로고    scopus 로고
    • Introduction à l'estimation Non-Paramétrique
    • Berlin: Springer
    • Tsybakov A.B. Introduction à l'estimation Non-Paramétrique 2003 Springer Berlin
    • (2003)
    • Tsybakov, A.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.