Johnstone, I.M.: Minimax Bayes, asymptotic minimax and sparse wavelet priors. Statistical Decision Theory and Related Topics V (pp. 303–326). Berlin Heidelberg New York: Springer 1994

Donoho, D.L., Liu, R.C., MacGibbon, K.B.: Minimax risk over hyperrectangles, and implications. Ann. Stat.18, 1416–1437 (1990)

Nemirovskii, A.S., Polyak, B.T., Tsybakov, A.B.: Rate of convergence of non-parametric estimates of maximum-likelihood type. Prob. Inf. Transm.21, 258–272 (1985)

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Donoho, D.L., Johnstone, I.M., Hoch, J.C., Stern, A.S.: Maximum Entropy and the Nearly Black Image. J. R. Stat. Soc. Ser. B54, 41–81 (1992) with discussion

Donoho, D.L., Johnstone, I.M.: Minimax risk overl p -balls forl q -error (Technical Report) Department of Statistics. Stanford: Stanford University 1992

Donoho, D.L.: Asymptotic minimax risk for sup-norm loss: solution via optimal recovery. Probab. Theory Relat. Fields (to appear, 1994)

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Donoho, D.J., Johnstone, I.M., Kerkyacharian, G., Picard, D.: Density estimation by wavelet thresholding. (Technical Report) Department of Statistics. Stanford: Stanford University 1993

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Sacks, J., Strawderman, W.E.: Improving on linear minimax estimates. (Stat. Decis. Theory Relat. Topics III, vol. 2 pp. 287–304) J.R. Stat. Soc., Ser. B (with discussion) (to appear, 1995) Berlin Heidelberg New York: Springer 1982

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Ibragimov, I.A., Hasminskii, R.Z.: On density estimation in the view of Kolmogorov's ideas in approximation theory. Ann. Stat.18, 999–1010 (1990)

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Donoho, D.L., Johnstone, I.M.: Minimax risk overl p -balls. (Technical Report No. 322) Department of Statistics, Stanford: Stanford University 1989

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Birgé, L., Massart, P.: Rates of convergence for minimum contrast estimators. Technical Report Université Paris VI. Probab. Theory Relat. Fields97, 113–150 (1993)

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Bickel, P.J.: Minimax estimation of the mean of a normal distribution when the parameter space is restricted. Ann. Stat.9, 1301–1309 (1981)

Donoho, D.L., Johnstone, I.M.: Minimax estimation via wavelet shrinkage. (Technical Report). Ann. Stat. (to appear, 1995a)

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Consider estimating the mean vector θ from dataN n (θ,σ 2 I) withl q norm loss,q≧1, when θ is known to lie in ann-dimensionall p ball,p∈(0, ∞). For largen, the ratio of minimaxlinear risk to minimax risk can bearbitrarily large ifp

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Brown, L.D.: Admissible estimators, recurrent diffusions, and insoluble boundary value problems. Ann. Math. Stat.42, 855–903 (1971)

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Korostelev, A.P.: Asymptotic minimax estimation of regression function in the uniform norm. Teor. Veoryatn. Priment.37 (in russian). Theory Probab. Appl.37 (1993) (in english)

Pinsker, M.S.: Optimal Filtration of square-integrable signals in Gaussian White Noise. Prob. Inf. Transm.16, 120–133 (1980)

Donoho, D.L., Johnstone, I.M. Minimax risk overl p -balls forl p -error. Probab. Th. Rel. Fields 99, 277–303 (1994). https://doi.org/10.1007/BF01199026

Ibragimov, I.A., Khasminskii, R.Z.: Nonparametric estimation of the value of a linear functional in a Gaussian white noise. Theory Probab. Appl.29, 1–32 (1984)

Feldman, I.: Constrained minimax estimation of the mean of the normal distribution with known variance. Ann. Stat.19, 2259–2265 (1991)

Brown, L.D., Johnstone, I.M., MacGibbon, K.B.: Variation Diminishing Transformations: A direct approach to total positivity and its statistical applications. J. Am. Stat. Assoc.76, 824–832 (1981)

Donoho, D.L., Johnstone, I.M.: Adapting to unknown smoothness via Wavelet shrinkage. J. Am. Stat. Assoc. (to appear, 1995b)