Robust Statistics—The Approach Based on Influence Functions

By J. Law. 1986

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Citations in the corpus

Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI (2019, neutral): “As stated in [165, 166, 167], stability is a must-have when drawing interpretations from a certain model.”
Security Evaluation of Support Vector Machines in Adversarial Environments (2014, background): “This has been also studied from a more theoretical perspective in [23], exploiting the framework of Robust Statistics [35, 50].”
Reinforcement learning (2019, positive): “11, we can use statistical tools such as the influence function (Hampel et al., 1986; Koh and Liang, 2017) to determine the state.”
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): “There is a large literature (see the books [Hub11, HRRS11, MMY06] for a comprehensive treat-ment) on robust statistics, with the goal of ﬁnding estimators that are stable under perturbations of the data.”
Learning from untrusted data (2016, neutral): “We expand on both the optimization error and statistical error bounds below.”
Being Robust (in High Dimensions) Can Be Practical (2017, background): “See (Huber & Ronchetti, 2009) and (Hampel et al., 1986) for further background.”
Asymptotic and Bootstrap Inference for Inequality and Poverty Measures (2007, background): “For more details, see the robust statistics literature (Tukey 1977, Huber 1981 and Hampel et al. 1986).”
Irregular Identification, Support Conditions, and Inverse Weight Estimation (2010, background): “Our main result in this section is that the “studentized” estimator converges to a standard normal (6)This is a property shared by the estimator in Heckman (1990b) and Andrews and Schafgans (1998) for an estimator of the intercept term in a sample selection model.”
Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count Data (2004, methodology): “Robust estimators with good properties have been available since at least the early 1980s for linear and generalized linear regression models (e.g., Huber 1981; Hampel et al. 1986; Stefanski, Carrol, and Ruppert 1986).”
Revisiting Methods for Finding Influential Examples (2021, methodology): “Influence functions (IFs) (Hampel 1986) are a core component of classic statistical theory and can be seen as approximations of leave one out (for convex functions), first used by Koh and Liang (2017) in the context of deep neural networks, and defined as:”
MINIMAX ESTIMATION OF A FUNCTIONAL ON A STRUCTURED (2016, background): “Functions x → χp(x) with this property are known as influence functions in semiparametric theory [2, 5, 13, 19, 31], go back to the von Mises calculus due to [38], and play an important role in robust statistics [9, 11], or [36], Chapter 20.”
Sharpening Wald-type inference in robust regression for small samples (2011, background): “For further reference see Hampel et al. (1986). Intuitively, this comes from a positive feedback loop: If observation i has a positive residual with ψ(ri/σ̂) < 0 and if the parameters are changed to slightly decrease the fitted value ŷi, then the residual ri increases and the influence of the observ”
Applying Robust Methods to Operational Risk Modeling (2006, methodology): “8”
Low-Income Immigrant Pupils Learning Vocabulary through Digital Picture Storybooks. (2010, methodology): “After Winsorizing one multivariate outlier on the expressive vocabulary test (Hampel, Ronchetti, Rousseeuw, & Stahel, 1986), assumptions for ANCOVA were met.”
Robust Super-resolution Volume Reconstruction from Slice Acquisitions: Application to Fetal Brain MRI (2010, background): “As a rule of thumb, if the scale parameter is the median absolute deviation of the error samples, an appropriate value of is 1.345 [37].”
Outliers in Questionnaire Data (2011, methodology): “An alternative to removing discordant observations is the use of robust statistics (e.g., Hampel et al., 1986; Rousseeuw & Leroy, 2003) to accommodate statistics for the presence of outliers.”
Complex Elliptically Symmetric Distributions: Survey, New Results and Applications (2012, methodology): “The real elliptically symmetric (RES) distributions have become a standard part of multivariate analysis and results for RES distributions are incorporated into most multivariate analysis textbooks [11], [40], [62] and textbooks on robust multivariate statistics [37], [60].”