Robust Estimators for the Parameters of Multivariate Lognormal Distribution

Abstract

In this paper, we introduce a class of location and scale estimators for the p-variate lognormal distribution. These estimators are obtained by applying a log transform to the data, computing robust Fisher consistent estimators for the obtained Gaussian data and transforming those estimators for the lognormal using the relationship between the parameters of both distributions. We prove some of the properties of these estimators, such as Fisher consistency, robustness and asymptotic normality.

Keywords:

• Multivariate lognormal distribution
• Influence function
• B-robustness

Acknowledgments

Helpful suggestions provided by Dr. Christophe Croux, as well as constructive comments and ideas from the referee are greately appreciated and have led to substantial improvements in the paper.