Robust Estimation of a Location Parameter

By Philippe Huber. 1964

This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)

Subfields: Statistics and Probability

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Citations in the corpus

DeepStack: Expert-level artificial intelligence in heads-up no-limit poker (2017, methodology): “The networks were trained using the Adam gradient descent optimization procedure (34) with a Huber loss (35).”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “…the kernel density estimator (KDE) by replacing the squared loss L(k(xi, ·), g) = ‖g − k(xi, ·)‖2H in (3.24) by the loss which is less sensitive to outliers such as Huber loss (Huber 1964) and k is assumed to be non-negative and to integrate to one, e.g., Gaussian kernel and Student’s-t kernel.”
Sever: A Robust Meta-Algorithm for Stochastic Optimization (2018, background): “Additive corruptions essentially correspond to Huber’s contamination model [Hub64] in robust statistics.”
Gated-Attention Architectures for Task-Oriented Language Grounding (2017, methodology): “Both methods use Huber loss (Huber 1964) between the estimated policy and the optimal policy given by the policy oracle.”
From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification (2016, methodology): “Coincidentally, as we next show, the sparsemax loss in the binary case reduces to the Huber classiﬁcation loss, an important loss function in robust statistics (Huber, 1964).”
Anchor regression: Heterogeneous data meet causality (2018, methodology): “stribution. These heterogeneities or perturbations make it dicult to gain actionable knowledge that generalizes well to new data sets. Approaches to deal with inhomogeneities include robust methods [Huber, 1964, 1973], mixed eects models [Pinheiro and Bates, 2000], time-varying coecient models [Hast”
A General Optimization-based Framework for Local Odometry Estimation with Multiple Sensors (2019, unknown): “ρ(·) represents robust huber norm [21].”
Comparison of Robust Regression Methods in Linear Regression (2011, methodology): “The most common general method of robust regression is M-estimation, introduced by Huber (1964) that is nearly as efficient as OLS [10].”
Deep learning interpretation of echocardiograms (2019, methodology): “We investigated other variants of prediction loss (absolute loss, Huber loss 45 for regression and Focal loss 46 for classiﬁcation), and they did not improve performance.”
The comparison of L 1 and L 2 -norm minimization methods (2010, methodology): “Historically, L1-norm method is a robust alternative to least squares (Huber, 1964; Fuchs, 1981; Kampmann, 1989), but it has been criticized by some researches for reasons of indirect solution, redundant measurements which are virtually ignored and difficult calculation (Rousseeuw et al., 1986;…”
Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database (2016, methodology): “…to develop a computationally efficient approach to fit a GP distribution model to data, while Dupuis [1998] used a weighting scheme to introduce a generalization of the ML equations, referred to as optimal bias-robust estimator (OBRE) [see also Huber, 1964; Hampel, 1968, 1974; Hampel et al., 1986].”
Executive Extraversion: Career and Firm Outcomes (2018, unknown): “5 This loss function is closely related to the Huber (1964) loss function used in robust regression in statistics, which has optimal properties when the underlying distribution of the data is unknown.”
Aid and growth in Sub-Saharan Africa: Accounting for transmission mechanisms (2005, methodology): “Then weights are calculated based on absolute residuals, as proposed by Huber (1964).”
Mask2CAD: 3D Shape Prediction by Learning to Segment and Retrieve (2020, methodology): “Starting with the M i ◦ F i feature map for a detected object, the object translation is directly regressed with a Huber loss [18] as follows: The object rotation is simultaneously predicted; the rotation is ﬁrst classiﬁed to a set of K discretized rotation bins using cross entropy loss; this…”