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August 2015 Robustness to outliers in location–scale parameter model using log-regularly varying distributions
Alain Desgagné
Ann. Statist. 43(4): 1568-1595 (August 2015). DOI: 10.1214/15-AOS1316


Estimating the location and scale parameters is common in statistics, using, for instance, the well-known sample mean and standard deviation. However, inference can be contaminated by the presence of outliers if modeling is done with light-tailed distributions such as the normal distribution. In this paper, we study robustness to outliers in location–scale parameter models using both the Bayesian and frequentist approaches. We find sufficient conditions (e.g., on tail behavior of the model) to obtain whole robustness to outliers, in the sense that the impact of the outliers gradually decreases to nothing as the conflict grows infinitely. To this end, we introduce the family of log-Pareto-tailed symmetric distributions that belongs to the larger family of log-regularly varying distributions.


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Alain Desgagné. "Robustness to outliers in location–scale parameter model using log-regularly varying distributions." Ann. Statist. 43 (4) 1568 - 1595, August 2015.


Received: 1 August 2014; Revised: 1 January 2015; Published: August 2015
First available in Project Euclid: 17 June 2015

zbMATH: 1317.62025
MathSciNet: MR3357871
Digital Object Identifier: 10.1214/15-AOS1316

Primary: 62F35
Secondary: 62F15

Keywords: Bayesian inference , Built-in robustness , log-Pareto-tailed symmetric distributions , log-regularly varying distributions , Outliers , theory of conflict resolution

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 4 • August 2015
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