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Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this distribution.
Fast mean estimation with sub-Gaussian rates
Cherapanamjeri, Y. and Flammarion, N. and Bartlett, P. L. (2019) · 1902
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PAC-Bayes under potentially heavy tails
Holland, M. J. (2019) · 1905
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Statistical Inference for Generative Models via Maximum Mean Discrepancy
Briol, F.-X., Barp, A. Duncan, A. B. and Girolami, M. (2019) · 1906
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Robust sub-Gaussian estimation of a mean vector in nearly linear time
Depersin, J., & Lecué, G. (2019) · 1906
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Distribution-robust mean estimation via smoothed random perturbations
Holland, M. J. (2019) · 1906
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Mean estimation and regression under heavy-tailed distributions–a survey
Lugosi, G., & Mendelson, S. (2019) · 1906
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A central limit corollary and a strong mixing condition
Rosenblatt, M., (1956) · 1956
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The minimum distance method
Wolfowitz, J. (1957) · 1957
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Robust covariance and scatter matrix estimation under Hüber’s contamination model
Chen, M., Gao, C., & Ren, Z. (2018) · 1960
Earlier work this paper cites.
Robust estimation of a location parameter
Hüber, P. J. (1964) · 1964
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On the assumptions used to prove asymptotic normality of maximum likelihood estimates
Le Cam, L. (1970) · 1970
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Convergence of estimates under dimensionality restrictions
Le Cam, L. (1973) · 1973
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On local and global properties in the theory of asymptotic normality of experiments
Le Cam, L. (1975) · 1974
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Mathematics and the picturing of data
Tukey, J. W. (1975) · 1975
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Another Look at Robustness: A Review of Reviews and Some New Developments
Bickel, P.J. (1976) · 1976
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Maximum likelihood from incomplete data via the EM algorithm
Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977) · 1977
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Minimum distance and robust estimation
Parr, W. C. & Schucany, W. R. (1980) · 1980
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Large sample properties of generalized method of moments estimators
Hansen, L. P. (1982) · 1982
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Approximation dans les espaces métriques et théorie de l’estimation
Birgé, L. (1983) · 1983
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Problem complexity and method efficiency in optimization
Nemirovski, A., & Yudin, B. (1983) · 1983
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Rates of convergence of minimum distance estimators and Kolmogorov’s entropy
Yatracos, Y. G. (1985) · 1985
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Random generation of combinatorial structures from a uniform distribution
Jerrum, M., Valiant, L., and Vazirani, V. (1986) · 1986
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On the method of bounded differences
McDiarmid, C. (1989) · 1989
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Mixing: properties and examples
Doukhan, P. (1994) · 1994
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Théorèmes limites pour des suites positivement ou faiblement dépendantes
Louhichi S. (1998) · 1998
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The consistency of posterior distributions in nonparametric problems
Barron, A., Schervish, M. J. and Wasserman, L. (1999) · 1999
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A new weak dependence condition and applications to moment inequalities
Doukhan, P., & Louhichi, S. (1999) · 1999
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Regression depth and center points
Amenta, N., Bern, M., Eppstein, D., and Teng, S.H. (2000) · 2000
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Asymptotic statistics
van der Vaart, A. W. (2000) · 2000
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Combinatorial methods in density estimation
Devroye, L., & Lugosi, G. (2001) · 2001
Earlier work this paper cites.
An optimal randomized algorithm for maximum Tukey depth
Chan, M.T. (2004) · 2004
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Model selection via testing: an alternative to (penalized) maximum likelihood estimators
Birgé, L. (2006) · 2006
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PAC-Bayes unleashed: generalisation bounds with unbounded losses
Haddouche, M., Guedj, B., Rivasplata, O. & Shawe-Taylor, J. (2020) · 2006
Cited alongside, same era.
Sparse density estimation with ℓ 1 \ell_{1} penalties
Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2007) · 2007
Cited alongside, same era.
Weak dependence: With examples and applications
Dedecker, J., Doukhan, P., Lang, G., Rafael, L. R. J., Louhichi, S., & Prieur, C. (2007) · 2007
Cited alongside, same era.
The space complexity of approximating the frequency moments
Alon, N. and Matias, Y. and Szegedy, M. (2008) · 2008
Cited alongside, same era.
Density estimation with quadratic loss: a confidence intervals method
Alquier, P. (2008) · 2008
Cited alongside, same era.
Learning via Hilbert Space Embedding of Distributions
A new method for estimation and model selection: ρ \rho -estimation
Baraud, Y., and Birgé, L., and Sart, M. (2017) · 2017
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Inference in generative models using the Wasserstein distance
Bernton, E., and Jacob, P. E., and Gerber, M., and Robert, C. P. (2017) · 2017
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Variational inference: A review for statisticians
Blei, D.M., Kucukelbir, A., and McAuliffe, J.D. (2017) · 2017
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Dimension free PAC-Bayesian bounds for the estimation of the mean of a random vector
Catoni, O. and Giulini, I. (2017) · 2017
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Optimal Kullback-Leibler Aggregation in Mixture Density Estimation by Maximum Likelihood
Dalalyan, A. S., & Sebbar, M. (2017) · 2017
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Song, L (2008) · 2008
Cited alongside, same era.
A fast, consistent kernel two-sample test
Gretton, A., Fukumizu, K., Harchaoui, Z., & Sriperumbudur, B. K. (2009) · 2009
Cited alongside, same era.
Robust stochastic approximation approach to stochastic programming
Nemirovski, A., Juditsky, A., Lan, G., & Shapiro, A. (2009) · 2009
Cited alongside, same era.
SPADES and mixture models
Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2010) · 2010
Cited alongside, same era.
Weakly dependent functional data
Hörmann, S. & Kokoszka, P. (2010) · 2010
Cited alongside, same era.
Hilbert space embeddings and metrics on probability measures,
Sriperumbudur, B. K., Gretton, A., Fukumizu, K., Schölkopf, B., & Lanckriet, G. R. (2010) · 2010
Cited alongside, same era.
Kernel belief propagation
Song, L., and Gretton, A., and Bickson, D., and Low, Y., & Guestrin, C. (2011) · 2011
Cited alongside, same era.
Du, S.S., Balakrishnan, S., and Singh, A. (2017) · 2017
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Robust PCA and pairs of projections in a Hilbert space
Giulini, I. (2017) · 2017
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Inconsistency of Bayesian inference for misspecified linear models, and a proposal for repairing it
Grünwald, P. D. and Van Ommen, T. (2017) · 2017
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A linear-time kernel goodness-of-fit test
Jitkrittum, W., Xu, W., Szabó, Z., Fukumizu, K., & Gretton, A. (2017) · 2017
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Kernel mean embedding of distributions: A review and beyond
Muandet, K., Fukumizu, K., Sriperumbudur, B., & Schölkopf, B. (2017) · 2017
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Inégalités de Hoeffding pour les fonctions lipschitziennes de suites dépendantes
Rio, E. (2017) · 2017
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Asymptotic theory of weakly dependent random processes
Rio, E. (2017) · 2017
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Minimax estimation of kernel mean embeddings
Tolstikhin, I., Sriperumbudur, B. K., & Muandet, K. (2017) · 2017
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InfoVAE: Information Maximizing Variational Autoencoders
Zhao, S., Song, J., & Ermon, S. (2017) · 2017
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Some theoretical properties of GANs
Biau, G., Cadre, B., Sangnier, M., & Tanielian, U. (2018) · 2018
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Consistency of variational Bayes inference for estimation and model selection in mixtures
Chérief-Abdellatif, B.-E. and Alquier, P. (2018) · 2018
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List-decodable robust mean estimation and learning mixtures of spherical gaussians
Diakonikolas, I., Kane, D.M., and Stewart, A. (2018) · 2018
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Efficient algorithms and lower bounds for robust linear regression
Diakonikolas, I., Kong, W., and Stewart, A. (2018) · 2018
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Robust dimension-free Gram operator estimates
Giulini, I. (2018) · 2018
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Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach
Huggins, J.H., Campbell, T., Kasprzak, M., & Broderick, T. (2018) · 2018
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Robust moment estimation and improved clustering via sum of squares
Kothari, P.K., Steinhardt, J., and Steurer, D. (2018) · 2018
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Minimax statistical learning with wasserstein distances
Lee, J., & Raginsky, M. (2018) · 2018
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Robust statistical learning with Lipschitz and convex loss functions
Chinot, G., Lecué, G., & Lerasle, M. (2019) · 2019
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Minimax estimation of a p p -dimensional linear functional in sparse Gaussian models and robust estimation of the mean
Collier, O., & Dalalyan, A. S. (2019) · 2019
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Robust Estimation and Generative Adversarial Nets
Gao, C., Liu, J., Yao, Y., and Zhu, W. (2019) · 2019
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Sub-Gaussian mean estimation in polynomial time
Hopkins, S. B. (2019) · 2019
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MONK – Outlier-Robust Mean Embedding Estimation by Median-of-Means
Lerasle, M., Szabó, Z., Mathieu, T., & Lecué, G. (2019) · 2019
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Jointly embedding multiple single-cell omics measurements
Liu, J., Huang, Y., Singh, R., Vert, J.-P., & Noble, W. S. (2019) · 2019
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MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy
Chérief-Abdellatif, B.-E. and Alquier, P. (2019) · 2020
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Robust classification via MOM minimization
Lecué, G., Lerasle, M., & Mathieu, T. (2020) · 2020
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On Minimax Optimality of GANs for Robust Mean Estimation
Wu, K., Ding, G. W., Huang, R. & Yu, Y. (2020) · 2020
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