Robust Estimation Using the Huber Function With a Data-Dependent Tuning Constant
- 1 June 2007
- journal article
- Published by Taylor & Francis Ltd in Journal of Computational and Graphical Statistics
- Vol. 16 (2), 468-481
- https://doi.org/10.1198/106186007x180156
Abstract
Robust estimation often relies on a dispersion function that is more slowly varying at large values than the square function. However, the choice of tuning constant in dispersion functions may impact the estimation efficiency to a great extent. For a given family of dispersion functions such as the Huber family, we suggest obtaining the “best” tuning constant from the data so that the asymptotic efficiency is maximized. This data-driven approach can automatically adjust the value of the tuning constant to provide the necessary resistance against outliers. Simulation studies show that substantial efficiency can be gained by this data-dependent approach compared with the traditional approach in which the tuning constant is fixed. We briefly illustrate the proposed method using two datasets.Keywords
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