2017/03/28 by Michaël Amiguet, Alfio Marazzi, Amiguet, Michael +5
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Fuzzy Systems and Optimization #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1703.09626
openalex publication_date 2017/03/28 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
Highly robust and efficient estimators for the generalized linear model with\na dispersion parameter are proposed. The estimators are based on three steps.\nIn the first step the maximum rank correlation estimator is used to\nconsistently estimate the slopes up to a scale factor. In the second step, the\nscale factor, the intercept, and the dispersion parameter are consistently\nestimated using a MT-estimator of a simple regression model. The combined\nestimator is highly robust but inefficient. Then, randomized quantile residuals\nbased on the initial estimators are used to detect outliers to be rejected and\nto define a set S of observations to be retained. Finally, a conditional\nmaximum likelihood (CML) estimator given the observations in S is computed. We\nshow that, under the model, S tends to the complete sample for increasing\nsample size. Therefore, the CML tends to the unconditional maximum likelihood\nestimator. It is therefore highly efficient, while maintaining the high degree\nof robustness of the initial estimator. The case of the negative binomial\nregression model is studied in detail.\n