Adaptive Huber Regression: Optimality and Phase Transition

[1]  Jianqing Fan,et al.  A NEW PERSPECTIVE ON ROBUST M-ESTIMATION: FINITE SAMPLE THEORY AND APPLICATIONS TO DEPENDENCE-ADJUSTED MULTIPLE TESTING. , 2017, Annals of statistics.

[2]  Stanislav Minsker.  Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries , 2016, The Annals of Statistics.

[3]  Jianqing Fan,et al.  I-LAMM FOR SPARSE LEARNING: SIMULTANEOUS CONTROL OF ALGORITHMIC COMPLEXITY AND STATISTICAL ERROR. , 2015, Annals of statistics.

[4]  Jianqing Fan,et al.  Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions , 2017, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[5]  Ilaria Giulini.  Robust Principal Component Analysis in Hilbert spaces , 2016, 1606.00187.

[6]  O. Catoni.  PAC-Bayesian bounds for the Gram matrix and least squares regression with a random design , 2016, 1603.05229.

[7]  Runze Li,et al.  A High-Dimensional Nonparametric Multivariate Test for Mean Vector , 2015, Journal of the American Statistical Association.

[8]  G. Lugosi,et al.  Sub-Gaussian mean estimators , 2015, 1509.05845.

[9]  Qi Zheng,et al.  GLOBALLY ADAPTIVE QUANTILE REGRESSION WITH ULTRA-HIGH DIMENSIONAL DATA. , 2015, Annals of statistics.

[10]  Trevor Hastie,et al.  Statistical Learning with Sparsity: The Lasso and Generalizations , 2015 .

[11]  G. Lugosi,et al.  Empirical risk minimization for heavy-tailed losses , 2014, 1406.2462.

[12]  Po-Ling Loh,et al.  Regularized M-estimators with nonconvexity: statistical and algorithmic theory for local optima , 2013, J. Mach. Learn. Res..

[13]  V. Spokoiny.  Bernstein - von Mises Theorem for growing parameter dimension , 2013, 1302.3430.

[14]  V. Spokoiny.  Parametric estimation. Finite sample theory , 2011, 1111.3029.

[15]  Sara van de Geer,et al.  Statistics for High-Dimensional Data: Methods, Theory and Applications , 2011 .

[16]  O. Catoni.  Challenging the empirical mean and empirical variance: a deviation study , 2010, 1009.2048.

[17]  Jiashun Jin,et al.  Robustness and accuracy of methods for high dimensional data analysis based on Student's t‐statistic , 2010, 1001.3886.

[18]  Martin J. Wainwright,et al.  Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using $\ell _{1}$ -Constrained Quadratic Programming (Lasso) , 2009, IEEE Transactions on Information Theory.

[19]  A. Belloni,et al.  L1-Penalized Quantile Regression in High Dimensional Sparse Models , 2009, 0904.2931.

[20]  P. Bickel,et al.  SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR , 2008, 0801.1095.

[21]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[22]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[23]  Q. Shao,et al.  On Parameters of Increasing Dimensions , 2000 .

[24]  Q. Shao,et al.  A general bahadur representation of M-estimators and its application to linear regression with nonstochastic designs , 1996 .

[25]  O. Lepskii.  Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates , 1992 .

[26]  E. Mammen.  Asymptotics with increasing dimension for robust regression with applications to the bootstrap , 1989 .

[27]  S. Portnoy.  Asymptotic behavior of M-estimators of p regression parameters when p , 1985 .

[28]  V. Yohai,et al.  ASYMPTOTIC BEHAVIOR OF M-ESTIMATORS FOR THE LINEAR MODEL , 1979 .

[29]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[30]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .