Initial robust estimation Generalized Linear Models

AGOSTINELLI, CLAUDIO; YOHAI, VICTOR, J.; VALDORA, MARINA

COMPUTATIONAL STATISTICS AND DATA ANALYSIS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2019 vol. 134 p. 144 - 156

0167-9473

Generalized Linear Models are routinely used in data analysis. Theclassical procedures for estimation are based on Maximum Likelihoodand it is well known that the presence of outliers can have a largeimpact on this estimator. Robust procedures are presented in theliterature but they need a robust initial estimate in order to be com-puted. This is especially important for robust procedures with nonconvex loss function such as redescending M-estimators. Subsamplingtechniques are often used to determine a robust initial estimate; how-ever when the number of unknown parameters is large the number ofsubsamples needed in order to have a high probability of having onesubsample free of outliers become infeasible. Furthermore the subsam-pling procedure provides a non deterministic starting point. Based onideas in Pe~na and Yohai [1999], we introduce a deterministic robustinitial estimate for M-estimators based on transformations [Valdoraand Yohai, 2014] for which we also develop an iteratively reweightedleast squares algorithm. The new methods are studied by Monte Carloexperiments.