References

Textbooks and expository articles on minimax theory

Tsybakov, A. (2008). Introduction to Nonparametric Estimation, Springer.
Yu. B. (1997) Assuad, Fano, and Le Cam, Festschrift for Lucien Le Cam, pdf.
John Duchi's notes on minimaxity from his class Statistics 311/Electrical Engineering 377.

Lecture 1, Tue Oct 27

Various minimax rates for sparse regression can be obtained

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.
Rigollet, P. and Tsybakov, A.B. (2012). Exponential screening and optimal rates of sparse estimation. Annals of Statistics, 39, 731-771.
E. J. Candès and M. A. Davenport. How well can we estimate a sparse vector? Applied and Computational Harmonic Analysis 34, 317--323.

Lecture 4, Tue Oct 27

Yang and Barron (1999). Information-theoretic determination of minimax rates of convergence, Annals of Statistics, 27(5), 1564-1599.

Lecture 7, Tue Nov 12

Wasserman, L. (2005). All of Nonparametric Statistics, Springer. Sections 7.8, 7.0, 7.10 and 7.11.
Tony Cai, Mark G. Low (2006), Adaptive Confidence Balls, Annals of Statistics, 34 (1), 202 - 228.
Baraud. Y. (2004). Confidence balls in Gaussian regression Ann. Statist. 32 (2004), no. 2, 528--551.

Lecture 8, Thu Nov 19

Ingster, I. and Suslina, I. A. (2003). Nonparametric Goodness-of-Fit Testing Under Gaussian Models Authors: Yu. I. Ingster, Springer. Sections 2.1 - 2.6.
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.
Addario-Berry, L., Broutin,N., Devroye, L., Lugosi, G (2010). On combinatorial testing problems, Annals of Statistics, 38(5),, 3063-3092.
Krishnamurthy, A. (2015). Minimaxity in Structured Normal Means Inference, arxiv: 1506.07902

Lecture 9, Tue Nov 24

Kim, J., Rinaldo, A. and Wasserman, L. (2015). Minimax rates for estimating the dimension of a manifold. preprint.
Castro, R. and Nowak, R. (2008). Minimax Bounds for Active Learning, IEEE, 54(5), 2339-2353.

Lecture 11, Tue Dec 1

Raskutti, G., Wainwright, M. and Yu, B. (2012). Minimax-Optimal Rates For Sparse Additive Models Over Kernel Classes Via Convex Programming, JMLR, 3(1), 389-427
Kirthevasan Kandasamy, Yaoliang Yu, (2015). Additive Approximations in High Dimensional Nonparametric Regression via the SALSA. df

Lecture 12, Thu Dec 3

Vu and Lei (2013). Minimax Rates of Estimation for Sparse PCA in High Dimensions, 1202.0786, AISTATS 2013
Vu and Lei (2013). Minimax sparse principal subspace estimation in high dimensions, Annals of Statistics, 41(6), 2905-2947.

Lecture 12, Thu Dec 3

Vu and Lei (2013). Minimax Rates of Estimation for Sparse PCA in High Dimensions, 1202.0786, AISTATS 2013
Vu and Lei (2013). Minimax sparse principal subspace estimation in high dimensions, Annals of Statistics, 41(6), 2905-2947.

Lecture 13, Tue Dec 8

Birnbaum, A., Johnstone, I.M., Nadler, B. and Debashis, P. (2013). Minimax bounds for sparse PCA with noisy high-dimensional data, Annals of Statistics, 41(3), 1055-1084.
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

Lecture 14, Thu Dec 10

Cai, T.T., Zhang, C-H., Zhou, H. H. (2010). Optimal rates of convergence for covariance matrix estimationi, Annals of Statistics, 38(4), 2118-2144.
Castro, E.A., Devenport, M. and Candes, E. (20113). On the Fundamental Limits of Adaptive Sensing, IEEE TRANSACTIONS ON INFORMATION THEORY, 59(1).