List of relevant papers

• E. J. Candès and M. A. Davenport. How well can we estimate a sparse vector? Applied and Computational Harmonic Analysis 34, 317--323.
• G. Raskutti, M. Wainwright, and B. Yu. Minimax rates of estimation for high-dimensional linear regression over lq balls. IEEE Transactions on Information Theory archive 57(10), 6976-6994.
• Ma, Z. and Wu, Y. (2015+) Volume ratio, sparsity, and minimaxity under unitarily invariant norms. arXiv:1306.3609. IEEE Trans Info Theory, to appear.
• Klopp, O., Tsybakov, AB., Verzelen, N. (2015). Oracle inequalities for network models and sparse graphon estimation. arxiv: 1507.04118
• Gao, C., Lu, Y. and Zhou, H. (2014). Rate-optimal graphon estimation. arxiv: 1410.5837.
• Anderson Y Zhang and Harrison H Zhou. Minimax rates of community detection in stochastic block model, arxiv: 1507.05313
• Privacy and statistical risk: Formalisms and minimax bounds. Rina Foygel Barber and John Duchi. arXiv:1406.1812
• Balakrishnan, S., Rinaldo, A., Sheehy, D., Singh, A., and Wasserman, L. (2011). Minimax Rates for Homology Inference. arxiv: 1112.5627
• Wei, W., Wainwright, M. and Ramchandrdan, K. (2010). Information-theoretic bounds on model selection for Gaussian Markov random fields, pdf.
• Vu and Lei (2013). Minimax sparse principal subspace estimation in high dimensions, Annals of Statistics, 41(6), 2905-2947.
• Vu and Lei (2013). Minimax Rates of Estimation for Sparse PCA in High Dimensions, 1202.0786, AISTATS 2013.
• Birnbaum, A., Johnstone, I.A., Nadler, B., and Paul, D. Minimax bounds for sparse PCA with noisy high-dimensional data, Ann. Statist., 41(3), 1055-1084.
• Cai, T., Zhang C.-H. and Zhou, H. (2010). Optimal Rates of Convergence for Covariance Matrix Estimation. Annals of Statistics, 38, 2118-2144, 2010.
• Cai, T., Ren, Z. and Zhou, H. (2010). Estimating Structured High-Dimensional Covariance and Precision Matrices: Optimal Rates and Adaptive Estimation, EJS
• N. Santhanam and M. J. Wainwright (2012). Information-theoretic limits of selecting binary graphical models in high dimensions. IEEE Transactions on Information Theory, 58(7): 4117--4134, July 2012.
• Genovese, C.R., Perone-Pacifico, M., Verdinelli, I. and Wasserman, Larry (2012). Minimax Manifold Estimation, JMLR 13, 1263-1291.
• Rigollet, P. and Tsybakov, A.B. (2012). Exponential screening and optimal rates of sparse estimation. Annals of Statistics, 39, 731-771.
• Cai. T. and Wu, Y. (2014). Optimal Detection of Sparse Mixtures Against a Given Null Distribution, IEEE, 60(4), 2217-2232.
• Yihong Wu and Pengkun Yang (2015). Chebyshev polynomials, moment matching, and optimal estimation of the unseen, arxiv: 1504.01227
• Han, Y., Jiao, J., Weissman, T. (2014). Minimax Estimation of Discrete Distributions under l1 Loss, arxiv: 1411.1467
• Arias-Castro, E., Candès, E.J., and Plan, Y. (2011). Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism, Ann. Statistics, 39(5), 2533-2556.
• Berthet, Q. and Rigollet, P. (2013). Optimal detection of sparse principal components in high dimension, Annals of Statistics 41(4), 1780-1815.
• Addario-Berry, L., Broutin,N., Devroye, L., Lugosi, G (2010). On combinatorial testing problems, Annals of Statistics, 38(5),, 3063-3092.
• Baraud, Y. (2002). Non-asymptotic minimax rates of testing in signal detection, Bernoulli 8(5), 577-606.
• Castro, E.A. and Verzelen, N. (2014). Community detection in dense random networks, Annals of Statistics 42(3), 940-969.
• Castro, E.A., Devenport, M. and Candes, E. (20113). On the Fundamental Limits of Adaptive Sensing, IEEE TRANSACTIONS ON INFORMATION THEORY, 59(1).
• Arias-Castro, E., Bubeck, S., Lugosi, G. and Verzelen, N. (2015). Detecting Markov Random Fields Hidden in White Noise, arxiv: 1504.06984.
• Zhou, Y. and Lafferty, J. (2015). Quantized Nonparametric Estimation, arxiv: 1503.0768.
• Ma, Z. and Wu, Y. (2015) Computational barriers in minimax submatrix detection. Ann Statist, Vol.43(3), pp.1089-1116.
• Yuchen Zhang, Martin J. Wainwright, Michael I. Jordan: Lower bounds on the performance of polynomial-time algorithms for sparse linear regression. COLT 2014: 921-948
• Wang, T., Berthet, Q. and Samworth, R.J. (2014). Statistical and computational trade-offs in estimation of sparse principal components, arxiv: 1408.5369
• Anything on minimax confidence sets...