메뉴 건너뛰기




Volumn 5, Issue 6, 1999, Pages 1099-1118

The asymptotic minimax constant for sup-norm loss in nonparametric density estimation

Author keywords

Density estimation; Exact constant; Optimal recovery; Uniform norm risk; White noise

Indexed keywords


EID: 0042112381     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318561     Document Type: Article
Times cited : (20)

References (17)
  • 2
    • 0032387073 scopus 로고    scopus 로고
    • Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2
    • Brown, L.D. and Zhang, C.-H. (1998) Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2. Ann. Statist., 26, 279-287
    • (1998) Ann. Statist. , vol.26 , pp. 279-287
    • Brown, L.D.1    Zhang, C.-H.2
  • 4
    • 21344480943 scopus 로고
    • Asymptotic minimax risk (for sup-norm loss):, solution via optimal recovery
    • Donoho, D. (1994) Asymptotic minimax risk (for sup-norm loss):, solution via optimal recovery. Probab. Theory Related Fields, 99, 145-170.
    • (1994) Probab. Theory Related Fields , vol.99 , pp. 145-170
    • Donoho, D.1
  • 6
    • 0009216977 scopus 로고
    • Bounds for the risks of non-parametric regression estimates
    • Ibragimov, I.A. and Khasminskii, R.Z. (1982) Bounds for the risks of non-parametric regression estimates. Theory Probab. Appl., 27, 84-99.
    • (1982) Theory Probab. Appl. , vol.27 , pp. 84-99
    • Ibragimov, I.A.1    Khasminskii, R.Z.2
  • 7
    • 0009387419 scopus 로고
    • A lower bound on the risk of non-parametric estimates of densities in the uniform metric
    • Khasminskii, R.Z. (1978) A lower bound on the risk 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
    • Khasminskii, R.Z.1
  • 8
    • 0000524793 scopus 로고
    • Exact asymptotically minimax estimator for nonparametric regression in uniform norm
    • Korostelev, A.P. (1993) Exact asymptotically minimax estimator for nonparametric regression in uniform norm. Theory Probab. Appl., 38, 775-782.
    • (1993) Theory Probab. Appl. , vol.38 , pp. 775-782
    • Korostelev, A.P.1
  • 10
    • 0001633551 scopus 로고    scopus 로고
    • On the solution of an optimal recovery problem and its applications in nonparametric regression
    • Leonov, S.L (1997) On the solution of an optimal recovery problem and its applications in nonparametric regression. Math. Methods Statist., 6, 476-490.
    • (1997) Math. Methods Statist. , vol.6 , pp. 476-490
    • Leonov, S.L.1
  • 11
    • 0002252004 scopus 로고
    • A survey of optimal recovery
    • C. Micchelli and T. Rivlin (eds), New York: Plenum Press
    • Micchelli, C. and Rivlin, T. (1977) A survey of optimal recovery. In C. Micchelli and T. Rivlin (eds), Optimal Estimation in Approximation Tlieory, pp. 1-54. New York: Plenum Press.
    • (1977) Optimal Estimation in Approximation Tlieory , pp. 1-54
    • Micchelli, C.1    Rivlin, T.2
  • 12
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and Gaussian white noise
    • Nussbaum, M. (1996) Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist., 24, 2399-2430.
    • (1996) Ann. Statist. , vol.24 , pp. 2399-2430
    • Nussbaum, M.1
  • 13
    • 0000056062 scopus 로고
    • Optimal filtering of square integrable signals in Gaussian white noise
    • Pinsker, M.S. (1980) Optimal filtering of square integrable signals in Gaussian white noise. Problems Inform. Transmission, 16, 120-133.
    • (1980) Problems Inform. Transmission , vol.16 , pp. 120-133
    • Pinsker, M.S.1
  • 15
    • 0000439527 scopus 로고
    • Optimal global rates of convergence for nonparametric regression
    • Stone, C. (1982) Optimal global rates of convergence for nonparametric regression. Ann. Statist., 10, 1040-1053.
    • (1982) Ann. Statist. , vol.10 , pp. 1040-1053
    • Stone, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.