Robust plug-in bandwidth estimators in nonparametric regression

Boente, Graciela; Fraiman, Ricardo; Meloche, J.

doi:10.1016/s0378-3758(96)00039-0

Cited by 34 publications

(50 citation statements)

References 17 publications

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“…In this section, we will introduce a robust estimator of the derivative of order n which generalizes the proposal considered, when n ¼ 2, by Boente et al (1997). On the other hand, our proposal corrects the bias of the estimates considered by Ha¨rdle and Gasser (1985), when n42.…”

Section: Robust Estimation Of the Derivative Of Order Nmentioning

confidence: 89%

“…Our proposal corrects this bias by introducing a term involving estimates of the derivatives up to the order n À 2. As mentioned above, when n ¼ 2, Boente et al (1997) considered kernel-based estimates for the second derivative of the regression function to provide a robust bandwidth selector in the nonparametric regression setting.…”

Section: Robust Estimation Of the Derivative Of Order Nmentioning

confidence: 99%

“…Under regularity conditions, Boente et al (1997) showed that the robust estimates of the second derivatives of regression function converges to the second derivatives of regression function. In this section, we will consider the following assumptions to derive the weak consistency of the estimates b j ðnÞ R ðt; hÞ defined in (6):…”

Section: Consistencymentioning

confidence: 99%

“…The preliminary estimates of the kth derivatives b j ðkÞ R ðtÞ, 1pkpn À 2 can be defined as in Ha¨rdle and Gasser (1985) or Boente et al (1997), when k ¼ 1; 2, respectively. Conditions for the uniform consistency of these estimates are given therein and are easily derived by applying Theorem 3.1.…”

Section: Consistencymentioning

confidence: 99%

“…The sensitivity of the classical bandwidth selectors to anomalous data was discussed by several authors, such as, Leung et al (1993), Wang and Scott (1994), Boente et al (1997) and Cantoni and Ronchetti (2001). Ha¨rdle and Gasser (1984) (for fixed designs) and Hall and Jones (1990) (for random designs) studied approximations to the bias and variance of local M-estimates and considered the mean square error of a local M-estimate, obtaining the optimal bandwidth for it.…”

Section: Introductionmentioning

confidence: 99%

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Robust estimators of high order derivatives of regression functions

Boente

Rodríguez

2006

Statistics & Probability Letters

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Section: Robust Estimation Of the Derivative Of Order Nmentioning

confidence: 89%

Section: Robust Estimation Of the Derivative Of Order Nmentioning

confidence: 99%

Section: Consistencymentioning

confidence: 99%

Section: Consistencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust estimators of high order derivatives of regression functions

Boente

Rodríguez

2006

Statistics & Probability Letters

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Robust nonparametric regression: A review

Čı́žek

Sadikoglu

2019

WIREs Computational Stats

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Nonparametric regression methods provide an alternative approach to parametric estimation that requires only weak identification assumptions and thus minimizes the risk of model misspecification. In this article, we survey some nonparametric regression techniques, with an emphasis on kernel-based estimation, that are additionally robust to atypical and outlying observations. While the main focus lies on robust regression estimation, robust bandwidth selection and conditional scale estimation are discussed as well. Robust estimation in popular nonparametric models such as additive and varying-coefficient models is summarized too. The performance of the main methods is demonstrated on a real dataset. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical and Graphical Methods of Data Analysis > Nonparametric Methods K E Y W O R D S nonparametric regression, outliers, robust estimation 1 | INTRODUCTIONNonparametric regression models have received substantial attention in the theoretical and applied statistics literature over the last few decades. The underlying reason for their growing popularity and importance is that they do not rely on any particular form of the regression function characterizing the relationship between the dependent and explanatory variables and that they are thus robust to model misspecification. On the other hand, many classical nonparametric estimators are not robust in the sense that they are sensitive to atypical and outlying observations in the data. To address this, many authors have explored robust nonparametric regression estimation. As many nonparametric estimators of the regression function are local versions of the estimators of the location-scale model or the linear regression model, many initially proposed robust nonparametric regression estimators were inspired by the developments and construction of robust estimators in those two simple models, which we briefly recall in Section 1.1. Later, we introduce the main concepts of nonparametric regression in Section 1.2 and discuss the robust nonparametric methods from Section 2 on. | Robust estimation of the location and regression modelsConsider the simple univariate location-scale model Y = μ + σε, where Y is a continuously distributed univariate random variable, μ and σ are the location and scale parameters, respectively, and ϵ is an error term. For a random sample

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Smoothed Local L-Estimation With an Application

Čı́žek

2004

Theory and Applications of Recent Robust Methods

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Robust plug-in bandwidth estimators in nonparametric regression

Cited by 34 publications

References 17 publications

Robust estimators of high order derivatives of regression functions

Robust estimators of high order derivatives of regression functions

Robust nonparametric regression: A review

Smoothed Local L-Estimation With an Application

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