Robust Estimators of the Generalized Log-Gamma Distribution

• Published in: Technometrics Vol. 56; no. 1; pp. 92 - 101
• Main Authors: Agostinelli, Claudio, Marazzi, Alfio, Yohai, Victor J
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.02.2014; American Society for Quality and the American Statistical Association; American Society for Quality
• Subjects: Analytical estimating; Contamination; Density; Density estimation; Estimation methods; Estimators; Gamma rays; Inference; Maximum likelihood estimators; Minimum quantile distance estimators; Outliers; Quantiles; Statistical estimation; Weighted likelihood estimators; τ Estimators
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1080/00401706.2013.818578

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 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. Supplementary materials are available online.