Small-sample performance of the MTM and MWM estimators for the parameters of log-location-scale families

ABSTRACT

Log-location-scale families arise as parametric models in numerous areas of application (e.g., economics, insurance). Since outliers are common in real data sets, it is therefore important to use estimators that are robust. It was recently shown that for estimating parameters of the log-location-scale families, two methods - Trimmed (MTM) and Winsorized Moments (MWM) - offer reasonable trade-offs between robustness and efficiency when sample size is large. In this paper, we perform a simulation study to check their performance in samples as small as n = 10. For numerical examples, we consider the lognormal and log-logistic distributions and their $\epsilon$-contaminated neighbourhoods, as well as t₁₀ and log-Pareto-tailed-normal distributions. We also demonstrate how the formulas of MTMand MWM estimators can be adjusted to fit other log-location-scale families and their variants. Comparisons of estimators are made on the basis of three criteria: relative efficiency with respect to the maximum likelihood estimator, breakdown points and premium-protection plots.

KEYWORDS:

• Breakdown point
• log-location-scale families
• premium-protection plot
• relative efficiency
• robust estimation
• trimmed data
• winsorized data

Acknowledgements

The authors are very appreciative of valuable insights and useful comments provided by an anonymous referee, which helped to significantly improve the paper. Also, much of this work was completed while the first author was a Ph.D. student in the Department of Mathematical Sciences at the University of Wisconsin-Milwaukee.

Disclosure statement

No potential conflict of interest was reported by the authors.