Robust Estimators of the Generalized Log-Gamma Distribution

Abstract

We propose robust estimators of the generalized log-gamma distribution and, more generally, of location-shape-scale families of distributions. A (weighted) Qτ estimator minimizes a τ scale of the differences between empirical and theoretical quantiles. It is n1/2 consistent; unfortunately, it is not asymptotically normal and, therefore, inconvenient for inference. However, it is a convenient starting point for a one-step weighted likelihood estimator, where the weights are based on a disparity measure between the model density and a kernel density estimate. The one-step weighted likelihood estimator is asymptotically normal and fully efficient under the model. It is also highly robust under outlier contamination. Supplementary materials are available online.