On a robust local estimator for the scale function in heteroscedastic nonparametric regression

Boente, Graciela; Ruiz, Marcelo; Zamar, Ruben H.

doi:10.1016/j.spl.2010.03.015

Cited by 16 publications

(9 citation statements)

References 33 publications

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“…Robust estimates of scale are important for a range of applications, from true scale problems to outlier identification, and as auxiliary parameters for more involved analyses. Recent work concerning robust scale estimation includes Boente, Ruiz, and Zamar (2010) and Wu and Zuo (2008).…”

Section: Introductionmentioning

confidence: 99%

A robust scale estimator based on pairwise means

Tarr

Müller

Weber

2012

Journal of Nonparametric Statistics

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We propose a new robust scale estimator, the pairwise mean scale estimator P n , which in its most basic form is the interquartile range of the pairwise means. The use of pairwise means leads to a surprisingly high efficiency across many distributions of practical interest. The properties of P n are presented under a unified generalised L-statistics framework, which encompasses numerous other scale estimators. Extensions to P n are proposed, including taking the range of the middle τ × 100% instead of just the middle 50% of the pairwise means as well as trimming and Winsorising both the original data and the pairwise means. Furthermore, we have implemented a method using adaptive trimming, which achieves a maximal breakdown value. We investigate the efficiency properties of the pairwise mean scale estimator relative to a number of other established robust scale estimators over a broad range of distributions using the corresponding maximum likelihood estimates as a common base for comparison.

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Section: Introductionmentioning

confidence: 99%

A robust scale estimator based on pairwise means

Tarr

Müller

Weber

2012

Journal of Nonparametric Statistics

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“…( 2008 ) and Boente et al. ( 2010 ). Therefore, we set without loss of generality and drop it from the notation from now on.…”

Section: The Proposed Family Of Estimatorsmentioning

confidence: 94%

Robust and efficient estimation of nonparametric generalized linear models

Kalogridis

Claeskens

Aelst

2023

TEST

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Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these shortcomings, we introduce and study a family of nonparametric full-rank and lower-rank spline estimators that result from the minimization of a penalized density power divergence. The proposed class of estimators is easily implementable, offers high protection against outlying observations and can be tuned for arbitrarily high efficiency in the case of clean data. We show that under weak assumptions, these estimators converge at a fast rate and illustrate their highly competitive performance on a simulation study and two real-data examples. Supplementary Information The online version contains supplementary material available at 10.1007/s11749-023-00866-x.

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“…Henceforth, we shall place emphasis on estimating θ 0 , and assume that φ 0 , the dispersion parameter, is either known or suitably substituted. For popular GLMs such as logistic, Poisson and exponential models, φ 0 is indeed known whereas for other GLMs, e.g., with Gaussian or Gamma responses, φ 0 can be estimated without any model fitting with the resistant Rice-type estimators proposed by Ghement et al (2008) and Boente et al (2010). Therefore, we set φ 0 = 1 without loss of generality and drop it from the notation from now on.…”

Section: Density Power Divergencementioning

confidence: 99%

Robust and efficient estimation of nonparametric generalized linear models

Claeskens¹,

Kalogridis²,

Aelst³

2022

Preprint

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Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these shortcomings we introduce and study a family of nonparametric full rank and lower rank spline estimators that result from the minimization of a penalized power divergence. The proposed class of estimators is easily implementable, offers high protection against outlying observations and can be tuned for arbitrarily high efficiency in the case of clean data. We show that under weak assumptions these estimators converge at a fast rate and illustrate their highly competitive performance on a simulation study and two real-data examples.

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On a robust local estimator for the scale function in heteroscedastic nonparametric regression

Cited by 16 publications

References 33 publications

A robust scale estimator based on pairwise means

A robust scale estimator based on pairwise means

Robust and efficient estimation of nonparametric generalized linear models

Robust and efficient estimation of nonparametric generalized linear models

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