Robust Estimators of the Generalized Log-Gamma Distribution

CLAUDIO AGOSTINELLI; ALFIO MARAZZI; VÍCTOR J. YOHAI

TECHNOMETRICS

AMER STATISTICAL ASSOC

Lugar: Washington; Año: 2014 vol. 56 p. 92 - 101

0040-1706

We propose robust estimators of the generalized log-gamma distribution and, more generally, of location-shape-scale families of distributions. A (weighted) Q tau estimator minimizes a tau scale of the differences between empirical and theoretical quantiles. It is $n^1/2$ 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.