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Robust nonparametric regression: A review

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Abstract 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
The local constant and local linear estimates for the taxi occupancy in New York on Tuesdays (left panel) and Saturdays (right panel). The red‐dashed line and the blue solid line represent the local constant and local linear estimators, respectively; the two lines however overlap on most of their support and are almost indistinguishable from each other
[ Normal View | Magnified View ]
The local constant estimates for the taxi occupancy in New York on Tuesdays (left panel) and Saturdays (right panel). The red dashed line, dark‐green solid line, and purple long‐dashed line represent the local least‐squares, local median, and local Huber estimators, respectively
[ Normal View | Magnified View ]

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Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Statistical and Graphical Methods of Data Analysis > Robust Methods

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