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Volumn 24, Issue 6, 1996, Pages 2399-2430

Asymptotic equivalence of density estimation and Gaussian white noise

Author keywords

Asymptotic minimax risk; Curve estimation; Deficiency distance; Hungarian construction; Likelihood process; Nonparametric experiments

Indexed keywords


EID: 0030328670     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032181160     Document Type: Article
Times cited : (203)

References (30)
  • 1
    • 0000253324 scopus 로고
    • On minimax filtering over ellipsoids
    • BELITSER, E. and LEVIT, B. (1995). On minimax filtering over ellipsoids. Math. Methods Statist. 4 259-273.
    • (1995) Math. Methods Statist. , vol.4 , pp. 259-273
    • Belitser, E.1    Levit, B.2
  • 2
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • BROWN, L. D. and LOW, M. (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.2
  • 3
    • 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
  • 5
    • 0001573354 scopus 로고
    • Renormalization exponents and optimal pointwise rates of convergence
    • DONOHO, D. L. and LOW, M. (1992). Renormalization exponents and optimal pointwise rates of convergence. Ann. Statist. 20 944-970.
    • (1992) Ann. Statist. , vol.20 , pp. 944-970
    • Donoho, D.L.1    Low, M.2
  • 7
    • 0020152606 scopus 로고
    • Estimating a square integrable probability density of a random variable
    • EFROIMOVICH, S. YU. and PINSKER, M. S. (1982). Estimating a square integrable probability density of a random variable. Problems Inform. Transmission 18 172-189.
    • (1982) Problems Inform. Transmission , vol.18 , pp. 172-189
    • Efroimovich, S.Yu.1    Pinsker, M.S.2
  • 8
    • 38249011268 scopus 로고
    • Poisson approximation of empirical processes
    • FALK, M. and REISS, R.-D. (1992). Poisson approximation of empirical processes. Statist. Probab. Lett. 14 39-48.
    • (1992) Statist. Probab. Lett. , vol.14 , pp. 39-48
    • Falk, M.1    Reiss, R.-D.2
  • 9
    • 0040383049 scopus 로고
    • On minimax estimation of regression
    • In Russian
    • GOLUBEV, G. K. (1984). On minimax estimation of regression. Problems Inform. Transmission 20 56-64. (In Russian.)
    • (1984) Problems Inform. Transmission , vol.20 , pp. 56-64
    • Golubev, G.K.1
  • 10
    • 0012973790 scopus 로고
    • LAN in problems of nonparametric estimation of functions and lower bounds for quadratic risks
    • GOLUBEV, G. K. (1991). LAN in problems of nonparametric estimation of functions and lower bounds for quadratic risks. Theory Probab. Appl. 36 152-157.
    • (1991) Theory Probab. Appl. , vol.36 , pp. 152-157
    • Golubev, G.K.1
  • 11
    • 0003319119 scopus 로고
    • On the estimation of an infinite dimensional parameter in Gaussian white noise
    • IBRAGIMOV, I. A. and KHASMINSKI, R. Z. (1977). On the estimation of an infinite dimensional parameter in Gaussian white noise. Soviet Math. Dokl. 236 1053-1055.
    • (1977) Soviet Math. Dokl. , vol.236 , pp. 1053-1055
    • Ibragimov, I.A.1    Khasminski, R.Z.2
  • 12
    • 0002197597 scopus 로고
    • Komlos-major-tusnady approximation for the general empirical process and Haar expansions of classes of functions
    • KOLTCHINSKII, V. (1994). Komlos-Major-Tusnady approximation for the general empirical process and Haar expansions of classes of functions. J. Theoret. Probab. 7 73-118.
    • (1994) J. Theoret. Probab. , vol.7 , pp. 73-118
    • Koltchinskii, V.1
  • 13
    • 0000348715 scopus 로고
    • An asymptotically minimax regression estimate in the uniform norm up to an exact constant
    • KOROSTELEV, A. P. (1993). An asymptotically minimax regression estimate in the uniform norm up to an exact constant. Theory Probab. Appl. 38 737-743.
    • (1993) Theory Probab. Appl. , vol.38 , pp. 737-743
    • Korostelev, A.P.1
  • 15
    • 0039198454 scopus 로고
    • Sur l'approximation de familles de mesures par des familles gaussiennes
    • LE CAM, L. (1985). Sur l'approximation de familles de mesures par des familles gaussiennes. Ann. Inst. H. Poincaré 21 225-287.
    • (1985) Ann. Inst. H. Poincaré , vol.21 , pp. 225-287
    • Le Cam, L.1
  • 18
    • 0001917690 scopus 로고
    • Renormalization and white noise approximation for nonparametric functional estimation problems
    • Low, M. (1992). Renormalization and white noise approximation for nonparametric functional estimation problems. Ann. Statist. 20 545-554.
    • (1992) Ann. Statist. , vol.20 , pp. 545-554
    • Low, M.1
  • 19
    • 0011648817 scopus 로고
    • The statistical information contained in additional observations
    • MAMMEN, E. (1986). The statistical information contained in additional observations. Ann. Statist. 14 665-678.
    • (1986) Ann. Statist. , vol.14 , pp. 665-678
    • Mammen, E.1
  • 20
    • 0000229421 scopus 로고
    • Asymptotic minimax theorems for the sample distribution function
    • MILLAR, P. W. (1979). Asymptotic minimax theorems for the sample distribution function. Z. Wahrsch. Verw. Gebiete 48 233-252.
    • (1979) Z. Wahrsch. Verw. Gebiete , vol.48 , pp. 233-252
    • Millar, P.W.1
  • 24
    • 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
  • 26
    • 21344483842 scopus 로고
    • Local invariance principles and their application to density estimation
    • RIO, E. (1994). Local invariance principles and their application to density estimation. Probab. Theory Related Fields 98 21-45.
    • (1994) Probab. Theory Related Fields , vol.98 , pp. 21-45
    • Rio, E.1
  • 30
    • 0039198450 scopus 로고
    • On the maximum deviation of the sample density
    • WOODROOFE, M. (1967). On the maximum deviation of the sample density. Ann. Math. Statist. 38 475-481.
    • (1967) Ann. Math. Statist. , vol.38 , pp. 475-481
    • Woodroofe, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.