Fetching the paper…
Reading the bibliography…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis.
[author] Huber, P. J.P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics 35 73–101. \endbibitem
1964
Earlier work this paper cites.
[author] Lieb, E. H.E. H. (1973). Convex trace functions and the Wigner-Yanase-Dyson conjecture. Advances in Math. 11 267–288. \endbibitem
1973
Earlier work this paper cites.
[author] Maronna, R. A.R. A. (1976). Robust M-Estimators of Multivariate Location and Scatter. Ann. Statist. 4 51–67. \endbibitem
1976
Earlier work this paper cites.
[author] Nemirovski, A.A. and Yudin, D.D. (1983). Problem complexity and method efficiency in optimization. John Wiley & Sons Inc. \endbibitem
1983
Earlier work this paper cites.
[author] Jerrum, Mark RM. R., Valiant, Leslie GL. G. and Vazirani, Vijay VV. V. (1986). Random generation of combinatorial structures from a uniform distribution. Theoretical Computer Science 43 169–188. \endbibitem
1986
Earlier work this paper cites.
[author] Tyler, D. E.D. E. (1987). A distribution-free M-estimator of multivariate scatter. The Annals of Statistics 234–251. \endbibitem
1987
Earlier work this paper cites.
[author] Davies, L.L. (1992). The asymptotics of Rousseeuw’s minimum volume ellipsoid estimator. The Annals of Statistics 1828–1843. \endbibitem
1992
Earlier work this paper cites.
[author] Lepski, O.O. (1992). Asymptotically minimax adaptive estimation. I: Upper bounds. Optimally adaptive estimates. Theory of Probability & Its Applications 36 682–697. \endbibitem
1992
Earlier work this paper cites.
[author] Butler, R. W.R. W., Davies, P. L.P. L. and Jhun, M.M. (1993). Asymptotics for the minimum covariance determinant estimator. The Annals of Statistics 1385–1400. \endbibitem
1993
Earlier work this paper cites.
{binproceedings}
1996
Earlier work this paper cites.
[author] Bhatia, R.R. (1997). Matrix analysis. Springer. \endbibitem
1997
Earlier work this paper cites.
[author] Ahlswede, R.R. and Winter, A.A. (2002). Strong converse for identification via quantum channels. IEEE Trans. Inform. Theory 48 569–579. 10.1109/18.985947 \endbibitem
2002
Earlier work this paper cites.
[author] Vershynin, R.R. (2007). Non-Asymptotic Theory of Random Matrices: lecture notes. Available at http://www-personal.umich.edu/~romanv/teaching/2006-07/280/lec6.pdf . \endbibitem
2006
Earlier work this paper cites.
[author] Hubert, M.M., Rousseeuw, P. J.P. J. and Van Aelst, S.S. (2008). High-breakdown robust multivariate methods. Statistical Science 92–119. \endbibitem
2008
Earlier work this paper cites.
[author] Huber, P. J.P. J. and Ronchetti, E. M.E. M. (2009). Robust statistics, second ed. Wiley Series in Probability and Statistics. John Wiley & Sons Inc., Hoboken, NJ. 10.1002/9780470434697 \endbibitem
2009
Earlier work this paper cites.
[author] Lam, CliffordC. and Fan, JianqingJ. (2009). Sparsistency and rates of convergence in large covariance matrix estimation. Annals of statistics 37 4254. \endbibitem
2009
Earlier work this paper cites.
2009
Cited alongside, same era.
[author] Cai, T. T.T. T., Zhang, C. H.C. H. and Zhou, H. H.H. H. (2010). Optimal rates of convergence for covariance matrix estimation. The Annals of Statistics 38 2118–2144. \endbibitem
2010
Cited alongside, same era.
[author] Carlen, E.E. (2010). Trace inequalities and quantum entropy: an introductory course. Available at http://www.mathphys.org/AZschool/material/AZ09-carlen.pdf . \endbibitem
2010
Cited alongside, same era.
2010
Cited alongside, same era.
2015
Later among the works it cites.
[author] Minsker, S.S. (2015). Geometric median and robust estimation in Banach spaces. Bernoulli 21 2308–2335. \endbibitem
2015
Later among the works it cites.
2015
Later among the works it cites.
[author] Aleksandrov, Alexei BorisovichA. B. and Peller, Vladimir VsevolodovichV. V. (2016). Operator Lipschitz functions. Russian Mathematical Surveys 71 605. \endbibitem
2016
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
[author] Candès, E. J.E. J., Li, X.X., Ma, Y.Y. and Wright, J.J. (2011). Robust principal component analysis? Journal of the ACM (JACM) 58 11. \endbibitem
2011
Cited alongside, same era.
[author] Koltchinskii, V.V., Lounici, K.K. and Tsybakov, A. B.A. B. (2011). Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. The Annals of Statistics 39 2302–2329. \endbibitem
2011
Cited alongside, same era.
2011
Cited alongside, same era.
{binproceedings}
2012
Cited alongside, same era.
[author] Boucheron, StéphaneS., Lugosi, GáborG. and Massart, PascalP. (2013). Concentration inequalities: A nonasymptotic theory of independence. Oxford university press. \endbibitem
2013
Cited alongside, same era.
2013
Cited alongside, same era.
[author] Srivastava, N.N. and Vershynin, R.R. (2013). Covariance estimation for distributions with 2 + ε 2+\varepsilon moments. The Annals of Probability 41 3081–3111. \endbibitem
2013
Cited alongside, same era.
2014
Cited alongside, same era.
2016
Closest in time.
2016
Closest in time.
2016
Closest in time.
2016
Closest in time.
[author] Hsu, D.D. and Sabato, S.S. (2016). Loss Minimization and Parameter Estimation with Heavy Tails. Journal of Machine Learning Research 17 1-40. \endbibitem
2016
Closest in time.
2016
Closest in time.
2016
Closest in time.
[author] Joly, EmilienE., Lugosi, GáborG., Oliveira, Roberto ImbuzeiroR. I. et al. (2017). On the estimation of the mean of a random vector. Electronic Journal of Statistics 11 440–451. \endbibitem
2017
Closest in time.
[author] Koltchinskii, VladimirV. and Lounici, KarimK. (2017). Concentration inequalities and moment bounds for sample covariance operators. Bernoulli 23 110–133. \endbibitem
2017
Closest in time.
2017
Closest in time.