Optimally Bounded Score Functions for Generalized Linear Models with Applications to Logistic Regression.

Stefanski, Lukas; Carroll, R. J.; Ruppert, D.

doi:10.21236/ada160348

Cited by 7 publications

(9 citation statements)

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“…As for the breakdown point also for other robustness concepts only few results exist concerning robust estimation in nonlinear models (see Stefanski et al (1986), Carroll (1993, 1995), Carroll and Pederson (1993), Liese and Vajda (1994». Here the general robustness concept based on shrinking neighbourhoods were regarded. For that some results concerning optimal robust estimators and designs for nonlinear problems could be found.…”

Section: Discussionmentioning

confidence: 99%

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Robust Planning and Analysis of Experiments

Müller

1997

Lecture Notes in Statistics

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Section: Discussionmentioning

confidence: 99%

“…(t, {3) := (: f3 J1. (t, P)/ ~=(3)' (seeStefanski et al (1986),Miiller (1994b». Solutions of (5.34) can be calculated by Newton-Raphson iterations.…”

mentioning

confidence: 99%

Robust Planning and Analysis of Experiments

Müller

1997

Lecture Notes in Statistics

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“…The bias correction term

b false(X_{i}; β false)

is used to ensure Fisher consistency in the presence of

w_{i} false(β false)

. See Stefanski, Carroll, and Ruppert (), Carroll and Pederson (), Bianco and Yohai (), Künsch, Stefanski, and Carroll () among others for different choices of

w_{i} false(β false)

. Note that

γ

‐logistic does not belong to this class, since it uses

{Y_{i} - π false(X_{i}; false(γ + 1 false) β false)}

for bias correction.…”

Section: Characteristics Of γ‐Logistic Regressionmentioning

confidence: 99%

Robust Mislabel Logistic Regression without Modeling Mislabel Probabilities

2017

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Logistic regression is among the most widely used statistical methods for linear discriminant analysis. In many applications, we only observe possibly mislabeled responses. Fitting a conventional logistic regression can then lead to biased estimation.One common resolution is to fit a mislabel logistic regression model, which takes into consideration of mislabeled responses. Another common method is to adopt a robust M -estimation by down-weighting suspected instances. In this work, we propose a new robust mislabel logistic regression based on γ-divergence. Our proposal possesses two advantageous features: (1) It does not need to model the mislabel probabilities. (2) The minimum γ-divergence estimation leads to a weighted estimating equation without the need to include any bias correction term, i.e., it is automatically bias-corrected. These features make the proposed γ-logistic regression more robust in model fitting and more intuitive for model interpretation through a simple weighting scheme. Our method is also easy to implement, and two types of algorithms are included. Simulation studies and the Pima data application are presented to demonstrate the performance of γ-logistic regression.

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“…Other robust estimators for GLM are provided in Refs . A link between different estimators can be found in Ref .…”

Section: Generalized Linear Modelsmentioning

confidence: 99%

Robust statistics: a selective overview and new directions

Medina

Ronchetti

2015

WIREs Computational Stats

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Classical statistics relies largely on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are derived under these assumptions. Standard examples are least squares estimators in linear models and their extensions, maximum-likelihood estimators and the corresponding likelihood-based tests, and generalized methods of moments (GMM) techniques in econometrics. Robust statistics deals with deviations from the stochastic assumptions and their dangers for classical estimators and tests and develops statistical procedures that are still reliable and reasonably efficient in the presence of such deviations. It can be viewed as a statistical theory dealing with approximate parametric models by providing a reasonable compromise between the rigidity of a strict parametric approach and the potential difficulties of interpretation of a fully nonparametric analysis. Many classical procedures are well known for not being robust. These procedures are optimal when the assumed model holds exactly, but they are biased and/or inefficient when small deviations from the model are present. The statistical results obtained from standard classical procedures on real data applications can therefore be misleading. In this paper we will give a brief introduction to robust statistics by reviewing some basic general concepts and tools and by showing how they can be used in data analysis to provide an alternative complementary analysis with additional useful information. In this study, we focus on robust statistical procedures based on M-estimators and tests because they provide a unified statistical framework that complements the classical theory. Robust procedures will be discussed for standard models, including linear models, general linear model, and multivariate analysis. Some recent developments in high-dimensional statistics will also be outlined.

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Optimally Bounded Score Functions for Generalized Linear Models with Applications to Logistic Regression.

Cited by 7 publications

References 0 publications

Robust Planning and Analysis of Experiments

Robust Planning and Analysis of Experiments

Robust Mislabel Logistic Regression without Modeling Mislabel Probabilities

Robust statistics: a selective overview and new directions

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