Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach

By Abhik Ghosh, Ayanendranath Basu. 2015

58 citations recorded by the source corpus.

The density power divergence (DPD) measure, defined in terms of a single parameter α, has proved to be a popular tool in the area of robust estimation [1]. Recently, Ghosh and Basu [5] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observations. In this paper, we present an extensive numerical study to describe the performance of the method in the case of linear regression, the most common setup under the case of non-homogeneous data. In addition, we extend the existing methods for the selection of the optimal robustness tuning parameter from the case of independent and identically distributed (i.i.d.) data to the case of non-homogeneous observations. Proper selection of the tuning parameter is critical to the appropriateness of the resulting analysis. The selection of the optimal robustness tuning parameter is explored in the context of the linear regression problem with an extensive numerical study involving real and simulated data.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cf071afe345c5f2b1cfba7bd19fb0ee662e2ce1e

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In Statistics and Probability

1. Ayanendranath Basu
2. Abhijit Mandal
3. Leandro Pardo
4. Nirian Martín
5. Abhik Ghosh

Citations in the corpus

• Robust estimation in generalized linear models: the density power divergence approach (2014, methodology): “Ghosh and Basu (2013b) suggested, on the basis of an extensive simulation study that the choice of minimum density power divergence estimator with α = 0 .”
• A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator (2016, methodology): “Later Ghosh and Basu (2015) empirically concluded, while extending to the non-homogeneous setup, the choice βP = β̂0.”