Mathematics and the Picturing of Data

By J. Tukey. 1975

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Citations in the corpus

Byzantine Stochastic Gradient Descent (2018, background): “Optimization and learning in the presence of adversarial noise is a well-studied problem [4, 5, 15, 20, 22, 28].”
Sever: A Robust Meta-Algorithm for Stochastic Optimization (2018, background): “These issues have motivated work on high-dimensional robust statistics going back to Tukey [Tuk75].”
Robust Estimators in High Dimensions without the Computational Intractability (2016, neutral): “Keywords-unsupervised learning, statistical learning, density estimation robust algorithm I. INTRODUCTION”
Agnostic Estimation of Mean and Covariance (2016, background): “Such robust statistics have been proposed and studied for mean and covariance estimation in high dimension as well (see [Hub64, Tuk74, Mar76, SJD81, Don82, Dav87, HPL91, DG92, MSY92, MZ12, CGR15] and the references therein).”
Quantile tomography: using quantiles with multivariate data (2008, methodology): “this approach was adopted by Rousseeuw, Ruts and Tukey (1999) for their bivariate boxplot; indeed, the search is most easily accomplished in the location setting (in the absence of covariates), when depth levels sets are relatively quick to compute, and the search can be slightly sped up using the n”
Integrated depth for functional data: statistical properties and consistency (2016, background): “Among the well-known examples of depths are Tukey’s halfspace depth of Tukey [37] and the simplicial depth of Liu [21].”
Monge-Kantorovich Depth, Quantiles, Ranks and Signs (2014, background): “Liu–Zuo–Serfling axioms and Tukey’s halfspace depth.”
Adaptive Huber Regression (2017, methodology): “-contamination model (Huber 1964), for which a number of depth-based procedures have been developed since the groundbreaking work of Tukey (1975).”
Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels (2008, background): “Some well-known examples are the halfspace depth (Tukey, 1975), the Oja’s depth (Oja, 1983), the simplicial depth (Liu, 1990), and the projection depth (Zuo, 2003).”
Bootstrapping Phylogenetic Trees: Theory and Methods (2003, background): “Trees are high-dimensional parameters, even if they do not lie naturally in a Euclidean space, so the best frequentist confidence statements that can be made about them rely on the notion of a confidence region R α defined by statements of the form P(τ ∈ R α ) = 1 − α (Tukey, 1975).”
Letter-Value Plots: Boxplots for Large Data (2017, background): “Using location depths, introduced by Tukey (1975), letter values could be extended to bivariate situations, which would permit the inclusion of letter-values in bagplots (Rousseeuw, Ruts, and Tukey 1999; Wolf 2014).”
Depth and homogeneity in regional flood frequency analysis (2008, methodology): “Half-space depth [Tukey, 1975]: It is defined for x 2 R with respect to a probability P on R as:”
Galton, Edgeworth, Frisch, and prospects for quantile regression in econometrics (2000, background): “As Rousseeuw and Hubert elegantly demonstrate it may be viewed as a natural extension to regression of the halfspace depth ideas of Tukey (1975), Donoho and Gasko (1992).”
Multivariate Functional Halfspace Depth (2014, methodology): “…case, we define the finite-sample multivariate functional halfspace depth (MFHDN ) of a curve X ∈ C(U )K as in Definition 3 with D the sample halfspace depth based on {Y 1(t), . . . , YN (t)} (Tukey 1975), HD ( X(t); FY(t),N ) = 1 N min u∈RK,‖u‖=1 #{Yn(t), n = 1, . . . , N : u′Yn(t) u′ X(t)}.”