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Volumn 117, Issue 1, 2000, Pages 17-48

Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point

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EID: 0034399225     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050265     Document Type: Article
Times cited : (73)

References (33)
  • 1
    • 0003297436 scopus 로고
    • An introduction to continuity, extrema and related topics for general Gaussian processes
    • California: Hayward
    • Adler, R.J.: An Introduction to Continuity, Extrema and Related Topics for General Gaussian Processes. IMS Lecture Notes - Monograph Series, v. 12, California: Hayward (1990)
    • (1990) IMS Lecture Notes - Monograph Series , vol.12
    • Adler, R.J.1
  • 3
    • 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 Relat. Fields, 99, 145-170 (1994a)
    • (1994) Probab. Theory Relat. Fields , vol.99 , pp. 145-170
    • Donoho, D.1
  • 4
    • 21344492321 scopus 로고
    • Statistical estimation and optimal recovery
    • Donoho, D.: Statistical estimation and optimal recovery, Ann. Statist., 22, 238-270 (1994b)
    • (1994) Ann. Statist. , vol.22 , pp. 238-270
    • Donoho, D.1
  • 5
    • 0001573354 scopus 로고
    • Renormalization exponents and optimal pointwise rates of convergence
    • Donoho, D., Low, M.: Renormalization exponents and optimal pointwise rates of convergence, Ann. Statist., 20, 944-970 (1992)
    • (1992) Ann. Statist. , vol.20 , pp. 944-970
    • Donoho, D.1    Low, M.2
  • 6
    • 0013086459 scopus 로고
    • Minimax detection of a signal in a white Gaussian noise
    • Ermakov, M.S.: Minimax detection of a signal in a white Gaussian noise, Theory Probab. Appl., 35, 667-679 (1990)
    • (1990) Theory Probab. Appl. , vol.35 , pp. 667-679
    • Ermakov, M.S.1
  • 7
    • 0001392090 scopus 로고
    • Optimization of relay systems via various performance indices
    • Fuller, A.T.: Optimization of relay systems via various performance indices. In: Proc. 1st International IFAC Congress, Moscow v. 2, 584-607 (1960)
    • (1960) Proc. 1st International IFAC Congress, Moscow , vol.2 , pp. 584-607
    • Fuller, A.T.1
  • 8
    • 0001569683 scopus 로고
    • Exact constants in inequalities between norms of the derivatives of a function
    • Gabushin, V.N.: Exact constants in inequalities between norms of the derivatives of a function, Math. Notes, 4, 221-232 (1968)
    • (1968) Math. Notes , vol.4 , pp. 221-232
    • Gabushin, V.N.1
  • 9
    • 0007189558 scopus 로고
    • Best approximation of functional on some sets
    • Gabushin, V.M.: Best approximation of functional on some sets, Math. Notes, 8, 551-562 (1970)
    • (1970) Math. Notes , vol.8 , pp. 551-562
    • Gabushin, V.M.1
  • 11
    • 0020112203 scopus 로고
    • Minimax nonparametric detection of signals in white Gaussian noise
    • Ingster, Yu.I.: Minimax nonparametric detection of signals in white Gaussian noise, Problems of Information Transmission, 18, 130-140 (1982)
    • (1982) Problems of Information Transmission , vol.18 , pp. 130-140
    • Ingster, Yu.I.1
  • 14
    • 0003058689 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives, I, II, III
    • Ingster, Yu.I.: Asymptotically minimax hypothesis testing for nonparametric alternatives, I, II, III. Math. Methods of Statist., 2, 85-114; 171-189; 249-268 (1993)
    • (1993) Math. Methods of Statist. , vol.2 , pp. 85-114
    • Ingster, Yu.I.1
  • 16
    • 0006381054 scopus 로고
    • Convergence rate of maximum deviation distributions of Gaussian processes and empirical densities, I
    • Konakov, V.D., Piterbarg, V.I.: Convergence rate of maximum deviation distributions of Gaussian processes and empirical densities, I. Theory Probab. Appl., 27, 759-779 (1983)
    • (1983) Theory Probab. Appl. , vol.27 , pp. 759-779
    • Konakov, V.D.1    Piterbarg, V.I.2
  • 17
    • 0002038546 scopus 로고
    • On the convergence rate of maximal deviation distribution for kernel regression estimates
    • Konakov, V.D., Piterbarg, V.I.: On the convergence rate of maximal deviation distribution for kernel regression estimates, J. Multivariate Anal., 15, 279-294 (1984)
    • (1984) J. Multivariate Anal. , vol.15 , pp. 279-294
    • Konakov, V.D.1    Piterbarg, V.I.2
  • 18
    • 0000348715 scopus 로고
    • Asymptotically minimax regression estimator in the uniform norm up to exact constant
    • Korostelev, A.P.: Asymptotically minimax regression estimator in the uniform norm up to exact constant, Theory Probab. Appl., 38, 737-743 (1993)
    • (1993) Theory Probab. Appl. , vol.38 , pp. 737-743
    • Korostelev, A.P.1
  • 19
    • 0030514782 scopus 로고    scopus 로고
    • A minimaxity criterion in nonparametric regression based on large deviation probabilities
    • Korostelev, A.P.: A minimaxity criterion in nonparametric regression based on large deviation probabilities, Ann. Statist., 24, 1075-1083 (1996)
    • (1996) Ann. Statist. , vol.24 , pp. 1075-1083
    • Korostelev, A.P.1
  • 21
    • 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. Meth. Statist. 6, 476-490 (1997)
    • (1997) Math. Meth. Statist. , vol.6 , pp. 476-490
    • Leonov, S.L.1
  • 23
    • 0031327277 scopus 로고    scopus 로고
    • Optimal pointwise adaptive methods in nonparametric estimation
    • Lepski, O.V, Spokoiny, V.G.: Optimal pointwise adaptive methods in nonparametric estimation. Ann. Statist. 25, 2512-2546 (1997)
    • (1997) Ann. Statist. , vol.25 , pp. 2512-2546
    • Lepski, O.V.1    Spokoiny, V.G.2
  • 26
    • 84968505292 scopus 로고
    • Asymptotic properties of the maximum in a stationary Gaussian process
    • Pickands, J., III Asymptotic properties of the maximum in a stationary Gaussian process. Trans. Amer. Math. Soc., 145, 75-86 (1969)
    • (1969) Trans. Amer. Math. Soc. , vol.145 , pp. 75-86
    • Pickands J. III1
  • 27
    • 0000997747 scopus 로고
    • Spline smoothing: The equivalent variable kernel method
    • Silverman, B.W.: Spline smoothing: the equivalent variable kernel method, Ann. Statist., 12, 898-916 (1984)
    • (1984) Ann. Statist. , vol.12 , pp. 898-916
    • Silverman, B.W.1
  • 29
    • 0011603859 scopus 로고
    • Über integralungleichungen zwischen einer funktion und ihrer ableitung
    • Sz. Nagy, B.: Über Integralungleichungen zwischen einer Funktion und ihrer Ableitung, Acta Sci. Math., 10, 64-74 (1941)
    • (1941) Acta Sci. Math. , vol.10 , pp. 64-74
    • Sz. Nagy, B.1
  • 30
    • 0001330826 scopus 로고
    • Kolmogorov type inequalities and the best formulas of numerical differentiation
    • Taikov, L.V.: Kolmogorov type inequalities and the best formulas of numerical differentiation, Math. Notes, 4, 233-238 (1968)
    • (1968) Math. Notes , vol.4 , pp. 233-238
    • Taikov, L.V.1
  • 32
    • 0032243618 scopus 로고    scopus 로고
    • Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
    • Tsybakov, A.B.: Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes, Ann. Statist., 26, 2420-2469 (1998)
    • (1998) Ann. Statist. , vol.26 , pp. 2420-2469
    • Tsybakov, A.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.