Robustness to outliers in location-scale parameter model using log-regularly varying distributions

TL;DR

This paper investigates robust statistical methods for estimating location and scale parameters in the presence of outliers, introducing a new family of distributions that ensure robustness through tail behavior.

Contribution

It introduces log-regularly varying distributions, including log-Pareto-tailed distributions, providing conditions for robustness to outliers in Bayesian and frequentist models.

Findings

Sufficient conditions for robustness to outliers identified.

Log-regularly varying distributions ensure decreasing influence of outliers.

New distribution family enhances robustness in statistical inference.

Abstract

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.