In this paper we present a robust parameter estimation method for jointly estimating shape parameter α, scale parameter γ and location parameter δ of a symmetric stable distribution. The proposed estimation method is based on Probability Integral Transformation (PIT) and robust M-estimators....

The concept of breakdown point was introduced by Hodges (1967) and Hampel (1968, 1971) and still plays an important though at times a controversial role in robust statistics. It has proved most successful in the context of location, scale and regression problems. In this paper we argue that this...

We distinguish between three types of outliers in a one-way random effects model. These are formally described in terms of their position relative to the main part of the observations. We propose simple rules for identifying such outliers and give an example which involves median-based statistics.

A Monte Carlo simulation was used to generate data for a comparison of five robust regression estimation methods with ordinary least squares (OLS) under 36 different outlier data configurations. Two of the robust estimators, Least Absolute Value (LAV) estimation and MM estimation, are...